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<div class="titlepage"><div><div><h3 class="title">
<a name="math_toolkit.logs_and_tables.all_table"></a><a class="link" href="all_table.html" title="Tables of Error Rates for all Functions">Tables of Error
      Rates for all Functions</a>
</h3></div></div></div>
<div class="table">
<a name="math_toolkit.logs_and_tables.all_table.table_beta"></a><p class="title"><b>Table&#160;23.3.&#160;Error rates for beta</b></p>
<div class="table-contents"><table class="table" summary="Error rates for beta">
<colgroup>
<col>
<col>
<col>
<col>
<col>
</colgroup>
<thead><tr>
<th>
              </th>
<th>
                <p>
                  GNU C++ version 7.1.0<br> linux<br> double
                </p>
              </th>
<th>
                <p>
                  GNU C++ version 7.1.0<br> linux<br> long double
                </p>
              </th>
<th>
                <p>
                  Sun compiler version 0x5150<br> Sun Solaris<br> long double
                </p>
              </th>
<th>
                <p>
                  Microsoft Visual C++ version 14.1<br> Win32<br> double
                </p>
              </th>
</tr></thead>
<tbody>
<tr>
<td>
                <p>
                  Beta Function: Small Values
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
                  2.1:</em></span> <span class="red">Max = +INF&#949; (Mean = +INF&#949;) <a class="link" href="logs.html#errors_GNU_C_version_7_1_0_linux_double_beta_GSL_2_1_Beta_Function_Small_Values">And
                  other failures.</a>)</span><br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span>
                  Max = 1.14&#949; (Mean = 0.574&#949;))
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 2.86&#949; (Mean = 1.22&#949;)</span><br> <br>
                  (<span class="emphasis"><em>&lt;cmath&gt;:</em></span> Max = 364&#949; (Mean = 76.2&#949;))
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 2.86&#949; (Mean = 1.22&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 2.23&#949; (Mean = 1.14&#949;)</span>
                </p>
              </td>
</tr>
<tr>
<td>
                <p>
                  Beta Function: Medium Values
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 0.978&#949; (Mean = 0.0595&#949;)</span><br>
                  <br> (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 1.18e+03&#949; (Mean = 238&#949;))<br>
                  (<span class="emphasis"><em>Rmath 3.2.3:</em></span> Max = 1.09e+03&#949; (Mean = 265&#949;))
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 61.4&#949; (Mean = 19.4&#949;)</span><br> <br>
                  (<span class="emphasis"><em>&lt;cmath&gt;:</em></span> Max = 1.07e+03&#949; (Mean = 264&#949;))
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 107&#949; (Mean = 24.5&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 96.5&#949; (Mean = 22.4&#949;)</span>
                </p>
              </td>
</tr>
<tr>
<td>
                <p>
                  Beta Function: Divergent Values
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
                  2.1:</em></span> Max = 12.1&#949; (Mean = 1.99&#949;))<br> (<span class="emphasis"><em>Rmath
                  3.2.3:</em></span> Max = 176&#949; (Mean = 28&#949;))
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 8.99&#949; (Mean = 2.44&#949;)</span><br> <br>
                  (<span class="emphasis"><em>&lt;cmath&gt;:</em></span> Max = 128&#949; (Mean = 23.8&#949;))
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 18.8&#949; (Mean = 2.71&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 11.4&#949; (Mean = 2.19&#949;)</span>
                </p>
              </td>
</tr>
</tbody>
</table></div>
</div>
<br class="table-break"><div class="table">
<a name="math_toolkit.logs_and_tables.all_table.table_beta_incomplete_"></a><p class="title"><b>Table&#160;23.4.&#160;Error rates for beta (incomplete)</b></p>
<div class="table-contents"><table class="table" summary="Error rates for beta (incomplete)">
<colgroup>
<col>
<col>
<col>
<col>
<col>
</colgroup>
<thead><tr>
<th>
              </th>
<th>
                <p>
                  GNU C++ version 7.1.0<br> linux<br> double
                </p>
              </th>
<th>
                <p>
                  GNU C++ version 7.1.0<br> linux<br> long double
                </p>
              </th>
<th>
                <p>
                  Sun compiler version 0x5150<br> Sun Solaris<br> long double
                </p>
              </th>
<th>
                <p>
                  Microsoft Visual C++ version 14.1<br> Win32<br> double
                </p>
              </th>
</tr></thead>
<tbody>
<tr>
<td>
                <p>
                  Incomplete Beta Function: Small Values
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 11.1&#949; (Mean = 2.32&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 18.7&#949; (Mean = 3.19&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 9.94&#949; (Mean = 2.17&#949;)</span>
                </p>
              </td>
</tr>
<tr>
<td>
                <p>
                  Incomplete Beta Function: Medium Values
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 0.568&#949; (Mean = 0.0254&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 69.2&#949; (Mean = 13.4&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 174&#949; (Mean = 25&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 90&#949; (Mean = 12.7&#949;)</span>
                </p>
              </td>
</tr>
<tr>
<td>
                <p>
                  Incomplete Beta Function: Large and Diverse Values
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 0.999&#949; (Mean = 0.0325&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 6.84e+04&#949; (Mean = 2.76e+03&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 6.86e+04&#949; (Mean = 2.79e+03&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 633&#949; (Mean = 29.7&#949;)</span>
                </p>
              </td>
</tr>
<tr>
<td>
                <p>
                  Incomplete Beta Function: Small Integer Values
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 0.786&#949; (Mean = 0.0323&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 11.6&#949; (Mean = 3.6&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 51.8&#949; (Mean = 11&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 26&#949; (Mean = 6.28&#949;)</span>
                </p>
              </td>
</tr>
</tbody>
</table></div>
</div>
<br class="table-break"><div class="table">
<a name="math_toolkit.logs_and_tables.all_table.table_betac"></a><p class="title"><b>Table&#160;23.5.&#160;Error rates for betac</b></p>
<div class="table-contents"><table class="table" summary="Error rates for betac">
<colgroup>
<col>
<col>
<col>
<col>
<col>
</colgroup>
<thead><tr>
<th>
              </th>
<th>
                <p>
                  GNU C++ version 7.1.0<br> linux<br> double
                </p>
              </th>
<th>
                <p>
                  GNU C++ version 7.1.0<br> linux<br> long double
                </p>
              </th>
<th>
                <p>
                  Sun compiler version 0x5150<br> Sun Solaris<br> long double
                </p>
              </th>
<th>
                <p>
                  Microsoft Visual C++ version 14.1<br> Win32<br> double
                </p>
              </th>
</tr></thead>
<tbody>
<tr>
<td>
                <p>
                  Incomplete Beta Function: Small Values
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 0.676&#949; (Mean = 0.0302&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 9.92&#949; (Mean = 2.3&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 11.2&#949; (Mean = 2.94&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 8.94&#949; (Mean = 2.06&#949;)</span>
                </p>
              </td>
</tr>
<tr>
<td>
                <p>
                  Incomplete Beta Function: Medium Values
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 0.949&#949; (Mean = 0.098&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 63.5&#949; (Mean = 13.5&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 97.6&#949; (Mean = 24.3&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 90.6&#949; (Mean = 14.8&#949;)</span>
                </p>
              </td>
</tr>
<tr>
<td>
                <p>
                  Incomplete Beta Function: Large and Diverse Values
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 1.12&#949; (Mean = 0.0458&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 1.05e+05&#949; (Mean = 5.45e+03&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 1.04e+05&#949; (Mean = 5.46e+03&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 3.72e+03&#949; (Mean = 113&#949;)</span>
                </p>
              </td>
</tr>
<tr>
<td>
                <p>
                  Incomplete Beta Function: Small Integer Values
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 0.586&#949; (Mean = 0.0314&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 11.1&#949; (Mean = 3.65&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 103&#949; (Mean = 17.4&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 26.2&#949; (Mean = 6.36&#949;)</span>
                </p>
              </td>
</tr>
</tbody>
</table></div>
</div>
<br class="table-break"><div class="table">
<a name="math_toolkit.logs_and_tables.all_table.table_binomial_coefficient"></a><p class="title"><b>Table&#160;23.6.&#160;Error rates for binomial_coefficient</b></p>
<div class="table-contents"><table class="table" summary="Error rates for binomial_coefficient">
<colgroup>
<col>
<col>
<col>
<col>
<col>
</colgroup>
<thead><tr>
<th>
              </th>
<th>
                <p>
                  GNU C++ version 7.1.0<br> linux<br> double
                </p>
              </th>
<th>
                <p>
                  GNU C++ version 7.1.0<br> linux<br> long double
                </p>
              </th>
<th>
                <p>
                  Sun compiler version 0x5150<br> Sun Solaris<br> long double
                </p>
              </th>
<th>
                <p>
                  Microsoft Visual C++ version 14.1<br> Win32<br> double
                </p>
              </th>
</tr></thead>
<tbody>
<tr>
<td>
                <p>
                  Binomials: small arguments
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 1&#949; (Mean = 0.369&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 1.5&#949; (Mean = 0.339&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 1.5&#949; (Mean = 0.339&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 1&#949; (Mean = 0.369&#949;)</span>
                </p>
              </td>
</tr>
<tr>
<td>
                <p>
                  Binomials: large arguments
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 0.939&#949; (Mean = 0.314&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 26.6&#949; (Mean = 6.13&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 53.2&#949; (Mean = 10.8&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 37.2&#949; (Mean = 7.4&#949;)</span>
                </p>
              </td>
</tr>
</tbody>
</table></div>
</div>
<br class="table-break"><div class="table">
<a name="math_toolkit.logs_and_tables.all_table.table_boost_math_powm1"></a><p class="title"><b>Table&#160;23.7.&#160;Error rates for boost::math::powm1</b></p>
<div class="table-contents"><table class="table" summary="Error rates for boost::math::powm1">
<colgroup>
<col>
<col>
<col>
<col>
<col>
</colgroup>
<thead><tr>
<th>
              </th>
<th>
                <p>
                  GNU C++ version 7.1.0<br> linux<br> long double
                </p>
              </th>
<th>
                <p>
                  GNU C++ version 7.1.0<br> linux<br> double
                </p>
              </th>
<th>
                <p>
                  Sun compiler version 0x5150<br> Sun Solaris<br> long double
                </p>
              </th>
<th>
                <p>
                  Microsoft Visual C++ version 14.1<br> Win32<br> double
                </p>
              </th>
</tr></thead>
<tbody><tr>
<td>
                <p>
                  powm1
                </p>
              </td>
<td>
                <p>
                  (<span class="emphasis"><em>&lt;math.h&gt;:</em></span> Max = 2.04&#949; (Mean = 0.493&#949;))<br>
                  <br> <span class="blue">Max = 2.04&#949; (Mean = 0.493&#949;)</span><br>
                  <br> (<span class="emphasis"><em>&lt;cmath&gt;:</em></span> Max = 2.04&#949; (Mean = 0.493&#949;))
                </p>
              </td>
<td>
                <p>
                  (<span class="emphasis"><em>Rmath 3.2.3:</em></span> Max = 1.06&#949; (Mean = 0.425&#949;))<br>
                  <br> (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 1.06&#949; (Mean = 0.425&#949;))<br>
                  <br> <span class="blue">Max = 1.06&#949; (Mean = 0.425&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 1.88&#949; (Mean = 0.49&#949;)</span><br> <br>
                  (<span class="emphasis"><em>&lt;math.h&gt;:</em></span> Max = 1.88&#949; (Mean = 0.49&#949;))
                </p>
              </td>
<td>
                <p>
                  (<span class="emphasis"><em>&lt;math.h&gt;:</em></span> Max = 1.84&#949; (Mean = 0.486&#949;))<br>
                  <br> <span class="blue">Max = 1.84&#949; (Mean = 0.486&#949;)</span>
                </p>
              </td>
</tr></tbody>
</table></div>
</div>
<br class="table-break"><div class="table">
<a name="math_toolkit.logs_and_tables.all_table.table_cbrt"></a><p class="title"><b>Table&#160;23.8.&#160;Error rates for cbrt</b></p>
<div class="table-contents"><table class="table" summary="Error rates for cbrt">
<colgroup>
<col>
<col>
<col>
<col>
<col>
</colgroup>
<thead><tr>
<th>
              </th>
<th>
                <p>
                  GNU C++ version 7.1.0<br> linux<br> double
                </p>
              </th>
<th>
                <p>
                  GNU C++ version 7.1.0<br> linux<br> long double
                </p>
              </th>
<th>
                <p>
                  Sun compiler version 0x5150<br> Sun Solaris<br> long double
                </p>
              </th>
<th>
                <p>
                  Microsoft Visual C++ version 14.1<br> Win32<br> double
                </p>
              </th>
</tr></thead>
<tbody><tr>
<td>
                <p>
                  cbrt Function
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 1.34&#949; (Mean = 0.471&#949;)</span><br> <br>
                  (<span class="emphasis"><em>&lt;cmath&gt;:</em></span> Max = 1.34&#949; (Mean = 0.471&#949;))<br>
                  (<span class="emphasis"><em>&lt;math.h&gt;:</em></span> Max = 1.34&#949; (Mean = 0.471&#949;))
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 1.34&#949; (Mean = 0.471&#949;)</span><br> <br>
                  (<span class="emphasis"><em>&lt;math.h&gt;:</em></span> Max = 1.34&#949; (Mean = 0.471&#949;))
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 1.7&#949; (Mean = 0.565&#949;)</span><br> <br>
                  (<span class="emphasis"><em>&lt;math.h&gt;:</em></span> Max = 1.7&#949; (Mean = 0.565&#949;))
                </p>
              </td>
</tr></tbody>
</table></div>
</div>
<br class="table-break"><div class="table">
<a name="math_toolkit.logs_and_tables.all_table.table_cos_pi"></a><p class="title"><b>Table&#160;23.9.&#160;Error rates for cos_pi</b></p>
<div class="table-contents"><table class="table" summary="Error rates for cos_pi">
<colgroup>
<col>
<col>
<col>
<col>
<col>
</colgroup>
<thead><tr>
<th>
              </th>
<th>
                <p>
                  GNU C++ version 7.1.0<br> linux<br> double
                </p>
              </th>
<th>
                <p>
                  GNU C++ version 7.1.0<br> linux<br> long double
                </p>
              </th>
<th>
                <p>
                  Sun compiler version 0x5150<br> Sun Solaris<br> long double
                </p>
              </th>
<th>
                <p>
                  Microsoft Visual C++ version 14.1<br> Win32<br> double
                </p>
              </th>
</tr></thead>
<tbody>
<tr>
<td>
                <p>
                  sin_pi and cos_pi
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 0.991&#949; (Mean = 0.302&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 0.991&#949; (Mean = 0.302&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 0.996&#949; (Mean = 0.284&#949;)</span>
                </p>
              </td>
</tr>
<tr>
<td>
                <p>
                  sin_pi and cos_pi near integers and half integers
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 0.976&#949; (Mean = 0.28&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 0.976&#949; (Mean = 0.28&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 0.996&#949; (Mean = 0.298&#949;)</span>
                </p>
              </td>
</tr>
</tbody>
</table></div>
</div>
<br class="table-break"><div class="table">
<a name="math_toolkit.logs_and_tables.all_table.table_cyl_bessel_i"></a><p class="title"><b>Table&#160;23.10.&#160;Error rates for cyl_bessel_i</b></p>
<div class="table-contents"><table class="table" summary="Error rates for cyl_bessel_i">
<colgroup>
<col>
<col>
<col>
<col>
<col>
</colgroup>
<thead><tr>
<th>
              </th>
<th>
                <p>
                  GNU C++ version 7.1.0<br> linux<br> double
                </p>
              </th>
<th>
                <p>
                  GNU C++ version 7.1.0<br> linux<br> long double
                </p>
              </th>
<th>
                <p>
                  Sun compiler version 0x5150<br> Sun Solaris<br> long double
                </p>
              </th>
<th>
                <p>
                  Microsoft Visual C++ version 14.1<br> Win32<br> double
                </p>
              </th>
</tr></thead>
<tbody>
<tr>
<td>
                <p>
                  Bessel I0: Mathworld Data
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
                  2.1:</em></span> Max = 270&#949; (Mean = 91.6&#949;) <a class="link" href="logs.html#errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_i_GSL_2_1_Bessel_I0_Mathworld_Data">And
                  other failures.</a>)<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span>
                  Max = 1.52&#949; (Mean = 0.622&#949;) <a class="link" href="logs.html#errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_i_Rmath_3_2_3_Bessel_I0_Mathworld_Data">And
                  other failures.</a>)
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 1.95&#949; (Mean = 0.738&#949;)</span><br> <br>
                  (<span class="emphasis"><em>&lt;cmath&gt;:</em></span> Max = 8.49&#949; (Mean = 3.46&#949;) <a class="link" href="logs.html#errors_GNU_C_version_7_1_0_linux_long_double_cyl_bessel_i__cmath__Bessel_I0_Mathworld_Data">And
                  other failures.</a>)
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 1.95&#949; (Mean = 0.661&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 0.762&#949; (Mean = 0.329&#949;)</span>
                </p>
              </td>
</tr>
<tr>
<td>
                <p>
                  Bessel I1: Mathworld Data
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
                  2.1:</em></span> Max = 128&#949; (Mean = 41&#949;) <a class="link" href="logs.html#errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_i_GSL_2_1_Bessel_I1_Mathworld_Data">And
                  other failures.</a>)<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span>
                  Max = 1.53&#949; (Mean = 0.483&#949;) <a class="link" href="logs.html#errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_i_Rmath_3_2_3_Bessel_I1_Mathworld_Data">And
                  other failures.</a>)
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 0.64&#949; (Mean = 0.202&#949;)</span><br> <br>
                  (<span class="emphasis"><em>&lt;cmath&gt;:</em></span> Max = 5&#949; (Mean = 2.15&#949;) <a class="link" href="logs.html#errors_GNU_C_version_7_1_0_linux_long_double_cyl_bessel_i__cmath__Bessel_I1_Mathworld_Data">And
                  other failures.</a>)
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 0.64&#949; (Mean = 0.202&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 0.767&#949; (Mean = 0.398&#949;)</span>
                </p>
              </td>
</tr>
<tr>
<td>
                <p>
                  Bessel In: Mathworld Data
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
                  2.1:</em></span> Max = 2.31&#949; (Mean = 0.838&#949;) <a class="link" href="logs.html#errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_i_GSL_2_1_Bessel_In_Mathworld_Data">And
                  other failures.</a>)<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span>
                  Max = 1.73&#949; (Mean = 0.601&#949;) <a class="link" href="logs.html#errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_i_Rmath_3_2_3_Bessel_In_Mathworld_Data">And
                  other failures.</a>)
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 1.8&#949; (Mean = 1.33&#949;)</span><br> <br>
                  (<span class="emphasis"><em>&lt;cmath&gt;:</em></span> Max = 430&#949; (Mean = 163&#949;) <a class="link" href="logs.html#errors_GNU_C_version_7_1_0_linux_long_double_cyl_bessel_i__cmath__Bessel_In_Mathworld_Data">And
                  other failures.</a>)
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 463&#949; (Mean = 140&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 3.46&#949; (Mean = 1.32&#949;)</span>
                </p>
              </td>
</tr>
<tr>
<td>
                <p>
                  Bessel Iv: Mathworld Data
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
                  2.1:</em></span> Max = 5.95&#949; (Mean = 2.08&#949;) <a class="link" href="logs.html#errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_i_GSL_2_1_Bessel_Iv_Mathworld_Data">And
                  other failures.</a>)<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span>
                  Max = 3.53&#949; (Mean = 1.39&#949;))
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 4.12&#949; (Mean = 1.85&#949;)</span><br> <br>
                  (<span class="emphasis"><em>&lt;cmath&gt;:</em></span> Max = 616&#949; (Mean = 221&#949;) <a class="link" href="logs.html#errors_GNU_C_version_7_1_0_linux_long_double_cyl_bessel_i__cmath__Bessel_Iv_Mathworld_Data">And
                  other failures.</a>)
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 4.12&#949; (Mean = 1.95&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 2.97&#949; (Mean = 1.24&#949;)</span>
                </p>
              </td>
</tr>
<tr>
<td>
                <p>
                  Bessel In: Random Data
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
                  2.1:</em></span> Max = 261&#949; (Mean = 53.2&#949;) <a class="link" href="logs.html#errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_i_GSL_2_1_Bessel_In_Random_Data">And
                  other failures.</a>)<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span>
                  Max = 7.37&#949; (Mean = 2.4&#949;))
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 4.62&#949; (Mean = 1.06&#949;)</span><br> <br>
                  (<span class="emphasis"><em>&lt;cmath&gt;:</em></span> Max = 645&#949; (Mean = 132&#949;))
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 176&#949; (Mean = 39.1&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 9.67&#949; (Mean = 1.88&#949;)</span>
                </p>
              </td>
</tr>
<tr>
<td>
                <p>
                  Bessel Iv: Random Data
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 0.661&#949; (Mean = 0.0441&#949;)</span><br>
                  <br> (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 6.18e+03&#949; (Mean = 1.55e+03&#949;)
                  <a class="link" href="logs.html#errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_i_GSL_2_1_Bessel_Iv_Random_Data">And
                  other failures.</a>)<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span>
                  <span class="red">Max = 4.28e+08&#949; (Mean = 2.85e+07&#949;))</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 8.35&#949; (Mean = 1.62&#949;)</span><br> <br>
                  (<span class="emphasis"><em>&lt;cmath&gt;:</em></span> Max = 1.05e+03&#949; (Mean = 224&#949;)
                  <a class="link" href="logs.html#errors_GNU_C_version_7_1_0_linux_long_double_cyl_bessel_i__cmath__Bessel_Iv_Random_Data">And
                  other failures.</a>)
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 283&#949; (Mean = 88.4&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 7.46&#949; (Mean = 1.71&#949;)</span>
                </p>
              </td>
</tr>
<tr>
<td>
                <p>
                  Bessel Iv: Mathworld Data (large values)
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
                  2.1:</em></span> Max = 37&#949; (Mean = 18&#949;) <a class="link" href="logs.html#errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_i_GSL_2_1_Bessel_Iv_Mathworld_Data_large_values_">And
                  other failures.</a>)<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span>
                  <span class="red">Max = 3.77e+168&#949; (Mean = 2.39e+168&#949;) <a class="link" href="logs.html#errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_i_Rmath_3_2_3_Bessel_Iv_Mathworld_Data_large_values_">And
                  other failures.</a>)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 14.7&#949; (Mean = 6.66&#949;)</span><br> <br>
                  (<span class="emphasis"><em>&lt;cmath&gt;:</em></span> Max = 118&#949; (Mean = 57.2&#949;) <a class="link" href="logs.html#errors_GNU_C_version_7_1_0_linux_long_double_cyl_bessel_i__cmath__Bessel_Iv_Mathworld_Data_large_values_">And
                  other failures.</a>)
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 14.7&#949; (Mean = 6.59&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 3.67&#949; (Mean = 1.64&#949;)</span>
                </p>
              </td>
</tr>
</tbody>
</table></div>
</div>
<br class="table-break"><div class="table">
<a name="math_toolkit.logs_and_tables.all_table.table_cyl_bessel_i_integer_orders_"></a><p class="title"><b>Table&#160;23.11.&#160;Error rates for cyl_bessel_i (integer orders)</b></p>
<div class="table-contents"><table class="table" summary="Error rates for cyl_bessel_i (integer orders)">
<colgroup>
<col>
<col>
<col>
<col>
<col>
</colgroup>
<thead><tr>
<th>
              </th>
<th>
                <p>
                  GNU C++ version 7.1.0<br> linux<br> double
                </p>
              </th>
<th>
                <p>
                  GNU C++ version 7.1.0<br> linux<br> long double
                </p>
              </th>
<th>
                <p>
                  Sun compiler version 0x5150<br> Sun Solaris<br> long double
                </p>
              </th>
<th>
                <p>
                  Microsoft Visual C++ version 14.1<br> Win32<br> double
                </p>
              </th>
</tr></thead>
<tbody>
<tr>
<td>
                <p>
                  Bessel I0: Mathworld Data (Integer Version)
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
                  2.1:</em></span> Max = 0.79&#949; (Mean = 0.482&#949;))<br> (<span class="emphasis"><em>Rmath
                  3.2.3:</em></span> Max = 1.52&#949; (Mean = 0.622&#949;) <a class="link" href="logs.html#errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_i_integer_orders__Rmath_3_2_3_Bessel_I0_Mathworld_Data_Integer_Version_">And
                  other failures.</a>)
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 1.95&#949; (Mean = 0.738&#949;)</span><br> <br>
                  (<span class="emphasis"><em>&lt;cmath&gt;:</em></span> Max = 8.49&#949; (Mean = 3.46&#949;) <a class="link" href="logs.html#errors_GNU_C_version_7_1_0_linux_long_double_cyl_bessel_i_integer_orders___cmath__Bessel_I0_Mathworld_Data_Integer_Version_">And
                  other failures.</a>)
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 1.95&#949; (Mean = 0.661&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 0.762&#949; (Mean = 0.329&#949;)</span>
                </p>
              </td>
</tr>
<tr>
<td>
                <p>
                  Bessel I1: Mathworld Data (Integer Version)
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
                  2.1:</em></span> Max = 0.82&#949; (Mean = 0.456&#949;))<br> (<span class="emphasis"><em>Rmath
                  3.2.3:</em></span> Max = 1.53&#949; (Mean = 0.483&#949;) <a class="link" href="logs.html#errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_i_integer_orders__Rmath_3_2_3_Bessel_I1_Mathworld_Data_Integer_Version_">And
                  other failures.</a>)
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 0.64&#949; (Mean = 0.202&#949;)</span><br> <br>
                  (<span class="emphasis"><em>&lt;cmath&gt;:</em></span> Max = 5&#949; (Mean = 2.15&#949;) <a class="link" href="logs.html#errors_GNU_C_version_7_1_0_linux_long_double_cyl_bessel_i_integer_orders___cmath__Bessel_I1_Mathworld_Data_Integer_Version_">And
                  other failures.</a>)
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 0.64&#949; (Mean = 0.202&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 0.767&#949; (Mean = 0.398&#949;)</span>
                </p>
              </td>
</tr>
<tr>
<td>
                <p>
                  Bessel In: Mathworld Data (Integer Version)
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
                  2.1:</em></span> Max = 5.15&#949; (Mean = 2.13&#949;) <a class="link" href="logs.html#errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_i_integer_orders__GSL_2_1_Bessel_In_Mathworld_Data_Integer_Version_">And
                  other failures.</a>)<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span>
                  Max = 1.73&#949; (Mean = 0.601&#949;) <a class="link" href="logs.html#errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_i_integer_orders__Rmath_3_2_3_Bessel_In_Mathworld_Data_Integer_Version_">And
                  other failures.</a>)
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 1.8&#949; (Mean = 1.33&#949;)</span><br> <br>
                  (<span class="emphasis"><em>&lt;cmath&gt;:</em></span> Max = 430&#949; (Mean = 163&#949;) <a class="link" href="logs.html#errors_GNU_C_version_7_1_0_linux_long_double_cyl_bessel_i_integer_orders___cmath__Bessel_In_Mathworld_Data_Integer_Version_">And
                  other failures.</a>)
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 463&#949; (Mean = 140&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 3.46&#949; (Mean = 1.32&#949;)</span>
                </p>
              </td>
</tr>
</tbody>
</table></div>
</div>
<br class="table-break"><div class="table">
<a name="math_toolkit.logs_and_tables.all_table.table_cyl_bessel_i_prime"></a><p class="title"><b>Table&#160;23.12.&#160;Error rates for cyl_bessel_i_prime</b></p>
<div class="table-contents"><table class="table" summary="Error rates for cyl_bessel_i_prime">
<colgroup>
<col>
<col>
<col>
<col>
<col>
</colgroup>
<thead><tr>
<th>
              </th>
<th>
                <p>
                  GNU C++ version 7.1.0<br> linux<br> double
                </p>
              </th>
<th>
                <p>
                  GNU C++ version 7.1.0<br> linux<br> long double
                </p>
              </th>
<th>
                <p>
                  Sun compiler version 0x5150<br> Sun Solaris<br> long double
                </p>
              </th>
<th>
                <p>
                  Microsoft Visual C++ version 14.1<br> Win32<br> double
                </p>
              </th>
</tr></thead>
<tbody>
<tr>
<td>
                <p>
                  Bessel I'0: Mathworld Data
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 0.82&#949; (Mean = 0.259&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 0.82&#949; (Mean = 0.259&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 0.82&#949; (Mean = 0.354&#949;)</span>
                </p>
              </td>
</tr>
<tr>
<td>
                <p>
                  Bessel I'1: Mathworld Data
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 1.97&#949; (Mean = 0.757&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 1.97&#949; (Mean = 0.757&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 1.36&#949; (Mean = 0.782&#949;)</span>
                </p>
              </td>
</tr>
<tr>
<td>
                <p>
                  Bessel I'n: Mathworld Data
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 2.31&#949; (Mean = 1.41&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 701&#949; (Mean = 212&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 3.61&#949; (Mean = 1.22&#949;)</span>
                </p>
              </td>
</tr>
<tr>
<td>
                <p>
                  Bessel I'v: Mathworld Data
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 1.62&#949; (Mean = 0.512&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 2.89e+03&#949; (Mean = 914&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 2.89e+03&#949; (Mean = 914&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 3.76e+03&#949; (Mean = 1.19e+03&#949;)</span>
                </p>
              </td>
</tr>
<tr>
<td>
                <p>
                  Bessel I'n: Random Data
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 3.95&#949; (Mean = 1.06&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 195&#949; (Mean = 37.1&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 9.85&#949; (Mean = 1.82&#949;)</span>
                </p>
              </td>
</tr>
<tr>
<td>
                <p>
                  Bessel I'v: Random Data
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 14.1&#949; (Mean = 2.93&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 336&#949; (Mean = 68.5&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 14&#949; (Mean = 2.5&#949;)</span>
                </p>
              </td>
</tr>
<tr>
<td>
                <p>
                  Bessel I'v: Mathworld Data (large values)
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 42.6&#949; (Mean = 20.2&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 42.6&#949; (Mean = 20.2&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 59.5&#949; (Mean = 26.6&#949;)</span>
                </p>
              </td>
</tr>
</tbody>
</table></div>
</div>
<br class="table-break"><div class="table">
<a name="math_toolkit.logs_and_tables.all_table.table_cyl_bessel_i_prime_integer_orders_"></a><p class="title"><b>Table&#160;23.13.&#160;Error rates for cyl_bessel_i_prime (integer orders)</b></p>
<div class="table-contents"><table class="table" summary="Error rates for cyl_bessel_i_prime (integer orders)">
<colgroup>
<col>
<col>
<col>
<col>
<col>
</colgroup>
<thead><tr>
<th>
              </th>
<th>
                <p>
                  GNU C++ version 7.1.0<br> linux<br> double
                </p>
              </th>
<th>
                <p>
                  GNU C++ version 7.1.0<br> linux<br> long double
                </p>
              </th>
<th>
                <p>
                  Sun compiler version 0x5150<br> Sun Solaris<br> long double
                </p>
              </th>
<th>
                <p>
                  Microsoft Visual C++ version 14.1<br> Win32<br> double
                </p>
              </th>
</tr></thead>
<tbody>
<tr>
<td>
                <p>
                  Bessel I'0: Mathworld Data (Integer Version)
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 0.82&#949; (Mean = 0.259&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 0.82&#949; (Mean = 0.259&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 0.82&#949; (Mean = 0.354&#949;)</span>
                </p>
              </td>
</tr>
<tr>
<td>
                <p>
                  Bessel I'1: Mathworld Data (Integer Version)
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 1.97&#949; (Mean = 0.757&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 1.97&#949; (Mean = 0.757&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 1.36&#949; (Mean = 0.782&#949;)</span>
                </p>
              </td>
</tr>
<tr>
<td>
                <p>
                  Bessel I'n: Mathworld Data (Integer Version)
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 2.31&#949; (Mean = 1.41&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 701&#949; (Mean = 212&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 3.61&#949; (Mean = 1.22&#949;)</span>
                </p>
              </td>
</tr>
</tbody>
</table></div>
</div>
<br class="table-break"><div class="table">
<a name="math_toolkit.logs_and_tables.all_table.table_cyl_bessel_j"></a><p class="title"><b>Table&#160;23.14.&#160;Error rates for cyl_bessel_j</b></p>
<div class="table-contents"><table class="table" summary="Error rates for cyl_bessel_j">
<colgroup>
<col>
<col>
<col>
<col>
<col>
</colgroup>
<thead><tr>
<th>
              </th>
<th>
                <p>
                  GNU C++ version 7.1.0<br> linux<br> long double
                </p>
              </th>
<th>
                <p>
                  GNU C++ version 7.1.0<br> linux<br> double
                </p>
              </th>
<th>
                <p>
                  Sun compiler version 0x5150<br> Sun Solaris<br> long double
                </p>
              </th>
<th>
                <p>
                  Microsoft Visual C++ version 14.1<br> Win32<br> double
                </p>
              </th>
</tr></thead>
<tbody>
<tr>
<td>
                <p>
                  Bessel J0: Mathworld Data
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 6.55&#949; (Mean = 2.86&#949;)</span><br> <br>
                  (<span class="emphasis"><em>&lt;cmath&gt;:</em></span> Max = 5.04&#949; (Mean = 1.78&#949;) <a class="link" href="logs.html#errors_GNU_C_version_7_1_0_linux_long_double_cyl_bessel_j__cmath__Bessel_J0_Mathworld_Data">And
                  other failures.</a>)
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
                  2.1:</em></span> Max = 0.629&#949; (Mean = 0.223&#949;) <a class="link" href="logs.html#errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_j_GSL_2_1_Bessel_J0_Mathworld_Data">And
                  other failures.</a>)<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span>
                  Max = 0.629&#949; (Mean = 0.223&#949;) <a class="link" href="logs.html#errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_j_Rmath_3_2_3_Bessel_J0_Mathworld_Data">And
                  other failures.</a>)
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 6.55&#949; (Mean = 2.86&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 2.52&#949; (Mean = 1.2&#949;)</span>
                </p>
              </td>
</tr>
<tr>
<td>
                <p>
                  Bessel J0: Mathworld Data (Tricky cases)
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 1.64e+08&#949; (Mean = 6.69e+07&#949;)</span><br>
                  <br> (<span class="emphasis"><em>&lt;cmath&gt;:</em></span> Max = 4.79e+08&#949; (Mean
                  = 1.96e+08&#949;))
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 8e+04&#949; (Mean = 3.27e+04&#949;)</span><br>
                  <br> (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 6.5e+07&#949; (Mean = 2.66e+07&#949;))<br>
                  (<span class="emphasis"><em>Rmath 3.2.3:</em></span> Max = 1.04e+07&#949; (Mean = 4.29e+06&#949;))
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 1.64e+08&#949; (Mean = 6.69e+07&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 1e+07&#949; (Mean = 4.09e+06&#949;)</span>
                </p>
              </td>
</tr>
<tr>
<td>
                <p>
                  Bessel J1: Mathworld Data
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 3.59&#949; (Mean = 1.33&#949;)</span><br> <br>
                  (<span class="emphasis"><em>&lt;cmath&gt;:</em></span> Max = 6.1&#949; (Mean = 2.95&#949;) <a class="link" href="logs.html#errors_GNU_C_version_7_1_0_linux_long_double_cyl_bessel_j__cmath__Bessel_J1_Mathworld_Data">And
                  other failures.</a>)
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
                  2.1:</em></span> Max = 6.62&#949; (Mean = 2.35&#949;) <a class="link" href="logs.html#errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_j_GSL_2_1_Bessel_J1_Mathworld_Data">And
                  other failures.</a>)<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span>
                  Max = 0.946&#949; (Mean = 0.39&#949;) <a class="link" href="logs.html#errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_j_Rmath_3_2_3_Bessel_J1_Mathworld_Data">And
                  other failures.</a>)
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 1.44&#949; (Mean = 0.637&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 1.73&#949; (Mean = 0.976&#949;)</span>
                </p>
              </td>
</tr>
<tr>
<td>
                <p>
                  Bessel J1: Mathworld Data (tricky cases)
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 2.18e+05&#949; (Mean = 9.76e+04&#949;)</span><br>
                  <br> (<span class="emphasis"><em>&lt;cmath&gt;:</em></span> Max = 2.15e+06&#949; (Mean
                  = 1.58e+06&#949;))
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 106&#949; (Mean = 47.5&#949;)</span><br> <br>
                  (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 8.75e+05&#949; (Mean = 5.32e+05&#949;))<br>
                  (<span class="emphasis"><em>Rmath 3.2.3:</em></span> Max = 2.93e+06&#949; (Mean = 1.7e+06&#949;))
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 2.18e+05&#949; (Mean = 9.76e+04&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 3.23e+04&#949; (Mean = 1.45e+04&#949;)</span>
                </p>
              </td>
</tr>
<tr>
<td>
                <p>
                  Bessel JN: Mathworld Data
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 6.85&#949; (Mean = 3.35&#949;)</span><br> <br>
                  (<span class="emphasis"><em>&lt;cmath&gt;:</em></span> <span class="red">Max = 2.13e+19&#949; (Mean
                  = 5.16e+18&#949;) <a class="link" href="logs.html#errors_GNU_C_version_7_1_0_linux_long_double_cyl_bessel_j__cmath__Bessel_JN_Mathworld_Data">And
                  other failures.</a>)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
                  2.1:</em></span> Max = 6.9e+05&#949; (Mean = 2.15e+05&#949;) <a class="link" href="logs.html#errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_j_GSL_2_1_Bessel_JN_Mathworld_Data">And
                  other failures.</a>)<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span>
                  <span class="red">Max = +INF&#949; (Mean = +INF&#949;) <a class="link" href="logs.html#errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_j_Rmath_3_2_3_Bessel_JN_Mathworld_Data">And
                  other failures.</a>)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 463&#949; (Mean = 112&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 14.7&#949; (Mean = 5.4&#949;)</span>
                </p>
              </td>
</tr>
<tr>
<td>
                <p>
                  Bessel J: Mathworld Data
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 14.7&#949; (Mean = 4.11&#949;)</span><br> <br>
                  (<span class="emphasis"><em>&lt;cmath&gt;:</em></span> Max = 3.49e+05&#949; (Mean = 8.09e+04&#949;)
                  <a class="link" href="logs.html#errors_GNU_C_version_7_1_0_linux_long_double_cyl_bessel_j__cmath__Bessel_J_Mathworld_Data">And
                  other failures.</a>)
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 10&#949; (Mean = 2.24&#949;)</span><br> <br>
                  (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 2.39e+05&#949; (Mean = 5.37e+04&#949;)
                  <a class="link" href="logs.html#errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_j_GSL_2_1_Bessel_J_Mathworld_Data">And
                  other failures.</a>)<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span>
                  <span class="red">Max = +INF&#949; (Mean = +INF&#949;) <a class="link" href="logs.html#errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_j_Rmath_3_2_3_Bessel_J_Mathworld_Data">And
                  other failures.</a>)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 14.7&#949; (Mean = 4.22&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 14.9&#949; (Mean = 3.89&#949;)</span>
                </p>
              </td>
</tr>
<tr>
<td>
                <p>
                  Bessel J: Mathworld Data (large values)
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 607&#949; (Mean = 305&#949;)</span><br> <br>
                  (<span class="emphasis"><em>&lt;cmath&gt;:</em></span> Max = 34.9&#949; (Mean = 17.4&#949;) <a class="link" href="logs.html#errors_GNU_C_version_7_1_0_linux_long_double_cyl_bessel_j__cmath__Bessel_J_Mathworld_Data_large_values_">And
                  other failures.</a>)
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 0.536&#949; (Mean = 0.268&#949;)</span><br> <br>
                  (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 4.91e+03&#949; (Mean = 2.46e+03&#949;)
                  <a class="link" href="logs.html#errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_j_GSL_2_1_Bessel_J_Mathworld_Data_large_values_">And
                  other failures.</a>)<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span>
                  Max = 5.9&#949; (Mean = 3.76&#949;))
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 607&#949; (Mean = 305&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 9.31&#949; (Mean = 5.52&#949;)</span>
                </p>
              </td>
</tr>
<tr>
<td>
                <p>
                  Bessel JN: Random Data
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 50.8&#949; (Mean = 3.69&#949;)</span><br> <br>
                  (<span class="emphasis"><em>&lt;cmath&gt;:</em></span> Max = 1.12e+03&#949; (Mean = 88.7&#949;))
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
                  2.1:</em></span> Max = 75.7&#949; (Mean = 5.36&#949;))<br> (<span class="emphasis"><em>Rmath
                  3.2.3:</em></span> Max = 3.93&#949; (Mean = 1.22&#949;))
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 99.6&#949; (Mean = 22&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 17.5&#949; (Mean = 1.46&#949;)</span>
                </p>
              </td>
</tr>
<tr>
<td>
                <p>
                  Bessel J: Random Data
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 11.4&#949; (Mean = 1.68&#949;)</span><br> <br>
                  (<span class="emphasis"><em>&lt;cmath&gt;:</em></span> Max = 501&#949; (Mean = 52.3&#949;))
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
                  2.1:</em></span> Max = 15.5&#949; (Mean = 3.33&#949;) <a class="link" href="logs.html#errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_j_GSL_2_1_Bessel_J_Random_Data">And
                  other failures.</a>)<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span>
                  Max = 6.74&#949; (Mean = 1.3&#949;))
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 260&#949; (Mean = 34&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 9.24&#949; (Mean = 1.17&#949;)</span>
                </p>
              </td>
</tr>
<tr>
<td>
                <p>
                  Bessel J: Random Data (Tricky large values)
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 785&#949; (Mean = 94.2&#949;)</span><br> <br>
                  (<span class="emphasis"><em>&lt;cmath&gt;:</em></span> <span class="red">Max = 5.01e+17&#949; (Mean
                  = 6.23e+16&#949;))</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
                  2.1:</em></span> Max = 2.48e+05&#949; (Mean = 5.11e+04&#949;))<br> (<span class="emphasis"><em>Rmath
                  3.2.3:</em></span> Max = 71.6&#949; (Mean = 11.7&#949;))
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 785&#949; (Mean = 97.4&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 59.2&#949; (Mean = 8.67&#949;)</span>
                </p>
              </td>
</tr>
</tbody>
</table></div>
</div>
<br class="table-break"><div class="table">
<a name="math_toolkit.logs_and_tables.all_table.table_cyl_bessel_j_integer_orders_"></a><p class="title"><b>Table&#160;23.15.&#160;Error rates for cyl_bessel_j (integer orders)</b></p>
<div class="table-contents"><table class="table" summary="Error rates for cyl_bessel_j (integer orders)">
<colgroup>
<col>
<col>
<col>
<col>
<col>
</colgroup>
<thead><tr>
<th>
              </th>
<th>
                <p>
                  GNU C++ version 7.1.0<br> linux<br> long double
                </p>
              </th>
<th>
                <p>
                  GNU C++ version 7.1.0<br> linux<br> double
                </p>
              </th>
<th>
                <p>
                  Sun compiler version 0x5150<br> Sun Solaris<br> long double
                </p>
              </th>
<th>
                <p>
                  Microsoft Visual C++ version 14.1<br> Win32<br> double
                </p>
              </th>
</tr></thead>
<tbody>
<tr>
<td>
                <p>
                  Bessel J0: Mathworld Data (Integer Version)
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 6.55&#949; (Mean = 2.86&#949;)</span><br> <br>
                  (<span class="emphasis"><em>&lt;cmath&gt;:</em></span> Max = 5.04&#949; (Mean = 1.78&#949;) <a class="link" href="logs.html#errors_GNU_C_version_7_1_0_linux_long_double_cyl_bessel_j_integer_orders___cmath__Bessel_J0_Mathworld_Data_Integer_Version_">And
                  other failures.</a>)
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
                  2.1:</em></span> Max = 1.12&#949; (Mean = 0.488&#949;))<br> (<span class="emphasis"><em>Rmath
                  3.2.3:</em></span> Max = 0.629&#949; (Mean = 0.223&#949;) <a class="link" href="logs.html#errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_j_integer_orders__Rmath_3_2_3_Bessel_J0_Mathworld_Data_Integer_Version_">And
                  other failures.</a>)
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 6.55&#949; (Mean = 2.86&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 2.52&#949; (Mean = 1.2&#949;)</span><br> <br>
                  (<span class="emphasis"><em>&lt;math.h&gt;:</em></span> Max = 1.89&#949; (Mean = 0.988&#949;))
                </p>
              </td>
</tr>
<tr>
<td>
                <p>
                  Bessel J0: Mathworld Data (Tricky cases) (Integer Version)
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 1.64e+08&#949; (Mean = 6.69e+07&#949;)</span><br>
                  <br> (<span class="emphasis"><em>&lt;cmath&gt;:</em></span> Max = 4.79e+08&#949; (Mean
                  = 1.96e+08&#949;))
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 8e+04&#949; (Mean = 3.27e+04&#949;)</span><br>
                  <br> (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 1e+07&#949; (Mean = 4.11e+06&#949;))<br>
                  (<span class="emphasis"><em>Rmath 3.2.3:</em></span> Max = 1.04e+07&#949; (Mean = 4.29e+06&#949;))
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 1.64e+08&#949; (Mean = 6.69e+07&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 1e+07&#949; (Mean = 4.09e+06&#949;)</span><br>
                  <br> (<span class="emphasis"><em>&lt;math.h&gt;:</em></span> <span class="red">Max
                  = 2.54e+08&#949; (Mean = 1.04e+08&#949;))</span>
                </p>
              </td>
</tr>
<tr>
<td>
                <p>
                  Bessel J1: Mathworld Data (Integer Version)
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 3.59&#949; (Mean = 1.33&#949;)</span><br> <br>
                  (<span class="emphasis"><em>&lt;cmath&gt;:</em></span> Max = 6.1&#949; (Mean = 2.95&#949;) <a class="link" href="logs.html#errors_GNU_C_version_7_1_0_linux_long_double_cyl_bessel_j_integer_orders___cmath__Bessel_J1_Mathworld_Data_Integer_Version_">And
                  other failures.</a>)
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
                  2.1:</em></span> Max = 1.89&#949; (Mean = 0.721&#949;))<br> (<span class="emphasis"><em>Rmath
                  3.2.3:</em></span> Max = 0.946&#949; (Mean = 0.39&#949;) <a class="link" href="logs.html#errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_j_integer_orders__Rmath_3_2_3_Bessel_J1_Mathworld_Data_Integer_Version_">And
                  other failures.</a>)
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 1.44&#949; (Mean = 0.637&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 1.73&#949; (Mean = 0.976&#949;)</span><br> <br>
                  (<span class="emphasis"><em>&lt;math.h&gt;:</em></span> Max = 11.4&#949; (Mean = 4.15&#949;))
                </p>
              </td>
</tr>
<tr>
<td>
                <p>
                  Bessel J1: Mathworld Data (tricky cases) (Integer Version)
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 2.18e+05&#949; (Mean = 9.76e+04&#949;)</span><br>
                  <br> (<span class="emphasis"><em>&lt;cmath&gt;:</em></span> Max = 2.15e+06&#949; (Mean
                  = 1.58e+06&#949;))
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 106&#949; (Mean = 47.5&#949;)</span><br> <br>
                  (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 1.26e+06&#949; (Mean = 6.28e+05&#949;))<br>
                  (<span class="emphasis"><em>Rmath 3.2.3:</em></span> Max = 2.93e+06&#949; (Mean = 1.7e+06&#949;))
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 2.18e+05&#949; (Mean = 9.76e+04&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 3.23e+04&#949; (Mean = 1.45e+04&#949;)</span><br>
                  <br> (<span class="emphasis"><em>&lt;math.h&gt;:</em></span> Max = 1.44e+07&#949; (Mean
                  = 6.5e+06&#949;))
                </p>
              </td>
</tr>
<tr>
<td>
                <p>
                  Bessel JN: Mathworld Data (Integer Version)
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 6.85&#949; (Mean = 3.35&#949;)</span><br> <br>
                  (<span class="emphasis"><em>&lt;cmath&gt;:</em></span> <span class="red">Max = 2.13e+19&#949; (Mean
                  = 5.16e+18&#949;) <a class="link" href="logs.html#errors_GNU_C_version_7_1_0_linux_long_double_cyl_bessel_j_integer_orders___cmath__Bessel_JN_Mathworld_Data_Integer_Version_">And
                  other failures.</a>)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
                  2.1:</em></span> Max = 6.9e+05&#949; (Mean = 2.53e+05&#949;) <a class="link" href="logs.html#errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_j_integer_orders__GSL_2_1_Bessel_JN_Mathworld_Data_Integer_Version_">And
                  other failures.</a>)<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span>
                  <span class="red">Max = +INF&#949; (Mean = +INF&#949;) <a class="link" href="logs.html#errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_j_integer_orders__Rmath_3_2_3_Bessel_JN_Mathworld_Data_Integer_Version_">And
                  other failures.</a>)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 463&#949; (Mean = 112&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 14.7&#949; (Mean = 5.4&#949;)</span><br> <br>
                  (<span class="emphasis"><em>&lt;math.h&gt;:</em></span> <span class="red">Max =
                  +INF&#949; (Mean = +INF&#949;) <a class="link" href="logs.html#errors_Microsoft_Visual_C_version_14_1_Win32_double_cyl_bessel_j_integer_orders___math_h__Bessel_JN_Mathworld_Data_Integer_Version_">And
                  other failures.</a>)</span>
                </p>
              </td>
</tr>
</tbody>
</table></div>
</div>
<br class="table-break"><div class="table">
<a name="math_toolkit.logs_and_tables.all_table.table_cyl_bessel_j_prime"></a><p class="title"><b>Table&#160;23.16.&#160;Error rates for cyl_bessel_j_prime</b></p>
<div class="table-contents"><table class="table" summary="Error rates for cyl_bessel_j_prime">
<colgroup>
<col>
<col>
<col>
<col>
<col>
</colgroup>
<thead><tr>
<th>
              </th>
<th>
                <p>
                  GNU C++ version 7.1.0<br> linux<br> double
                </p>
              </th>
<th>
                <p>
                  GNU C++ version 7.1.0<br> linux<br> long double
                </p>
              </th>
<th>
                <p>
                  Sun compiler version 0x5150<br> Sun Solaris<br> long double
                </p>
              </th>
<th>
                <p>
                  Microsoft Visual C++ version 14.1<br> Win32<br> double
                </p>
              </th>
</tr></thead>
<tbody>
<tr>
<td>
                <p>
                  Bessel J0': Mathworld Data
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 18.9&#949; (Mean = 6.82&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 18.9&#949; (Mean = 6.72&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 6.62&#949; (Mean = 2.55&#949;)</span>
                </p>
              </td>
</tr>
<tr>
<td>
                <p>
                  Bessel J0': Mathworld Data (Tricky cases)
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 7.44&#949; (Mean = 3.34&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 7.44&#949; (Mean = 3.31&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 3.67&#949; (Mean = 1.74&#949;)</span>
                </p>
              </td>
</tr>
<tr>
<td>
                <p>
                  Bessel J1': Mathworld Data
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 7.9&#949; (Mean = 3.37&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 7.9&#949; (Mean = 3.37&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 0.999&#949; (Mean = 0.627&#949;)</span>
                </p>
              </td>
</tr>
<tr>
<td>
                <p>
                  Bessel J1': Mathworld Data (tricky cases)
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 287&#949; (Mean = 129&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 5.88e+05&#949; (Mean = 2.63e+05&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 5.88e+05&#949; (Mean = 2.63e+05&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 288&#949; (Mean = 129&#949;)</span>
                </p>
              </td>
</tr>
<tr>
<td>
                <p>
                  Bessel JN': Mathworld Data
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 0.527&#949; (Mean = 0.128&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 1.29e+03&#949; (Mean = 312&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 1.29e+03&#949; (Mean = 355&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 14&#949; (Mean = 6.13&#949;)</span>
                </p>
              </td>
</tr>
<tr>
<td>
                <p>
                  Bessel J': Mathworld Data
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 21.5&#949; (Mean = 4.7&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 42.5&#949; (Mean = 9.31&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 42.5&#949; (Mean = 9.32&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 23.7&#949; (Mean = 8&#949;)</span>
                </p>
              </td>
</tr>
<tr>
<td>
                <p>
                  Bessel J': Mathworld Data (large values)
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 989&#949; (Mean = 495&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 989&#949; (Mean = 495&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 2.9&#949; (Mean = 1.61&#949;)</span>
                </p>
              </td>
</tr>
<tr>
<td>
                <p>
                  Bessel JN': Random Data
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 0.593&#949; (Mean = 0.0396&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 11.3&#949; (Mean = 1.85&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 79.4&#949; (Mean = 16.2&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 6.34&#949; (Mean = 0.999&#949;)</span>
                </p>
              </td>
</tr>
<tr>
<td>
                <p>
                  Bessel J': Random Data
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 0.885&#949; (Mean = 0.033&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 139&#949; (Mean = 6.47&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 279&#949; (Mean = 27.2&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 176&#949; (Mean = 9.75&#949;)</span>
                </p>
              </td>
</tr>
<tr>
<td>
                <p>
                  Bessel J': Random Data (Tricky large values)
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 474&#949; (Mean = 62.2&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 474&#949; (Mean = 64.5&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 379&#949; (Mean = 45.4&#949;)</span>
                </p>
              </td>
</tr>
</tbody>
</table></div>
</div>
<br class="table-break"><div class="table">
<a name="math_toolkit.logs_and_tables.all_table.table_cyl_bessel_j_prime_integer_orders_"></a><p class="title"><b>Table&#160;23.17.&#160;Error rates for cyl_bessel_j_prime (integer orders)</b></p>
<div class="table-contents"><table class="table" summary="Error rates for cyl_bessel_j_prime (integer orders)">
<colgroup>
<col>
<col>
<col>
<col>
<col>
</colgroup>
<thead><tr>
<th>
              </th>
<th>
                <p>
                  GNU C++ version 7.1.0<br> linux<br> double
                </p>
              </th>
<th>
                <p>
                  GNU C++ version 7.1.0<br> linux<br> long double
                </p>
              </th>
<th>
                <p>
                  Sun compiler version 0x5150<br> Sun Solaris<br> long double
                </p>
              </th>
<th>
                <p>
                  Microsoft Visual C++ version 14.1<br> Win32<br> double
                </p>
              </th>
</tr></thead>
<tbody>
<tr>
<td>
                <p>
                  Bessel J0': Mathworld Data (Integer Version)
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 18.9&#949; (Mean = 6.82&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 18.9&#949; (Mean = 6.72&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 6.62&#949; (Mean = 2.55&#949;)</span>
                </p>
              </td>
</tr>
<tr>
<td>
                <p>
                  Bessel J0': Mathworld Data (Tricky cases) (Integer Version)
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 7.44&#949; (Mean = 3.34&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 7.44&#949; (Mean = 3.31&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 3.67&#949; (Mean = 1.74&#949;)</span>
                </p>
              </td>
</tr>
<tr>
<td>
                <p>
                  Bessel J1': Mathworld Data (Integer Version)
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 7.9&#949; (Mean = 3.37&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 7.9&#949; (Mean = 3.37&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 0.999&#949; (Mean = 0.627&#949;)</span>
                </p>
              </td>
</tr>
<tr>
<td>
                <p>
                  Bessel J1': Mathworld Data (tricky cases) (Integer Version)
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 287&#949; (Mean = 129&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 5.88e+05&#949; (Mean = 2.63e+05&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 5.88e+05&#949; (Mean = 2.63e+05&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 288&#949; (Mean = 129&#949;)</span>
                </p>
              </td>
</tr>
<tr>
<td>
                <p>
                  Bessel JN': Mathworld Data (Integer Version)
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 0.527&#949; (Mean = 0.128&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 1.29e+03&#949; (Mean = 312&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 1.29e+03&#949; (Mean = 355&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 14&#949; (Mean = 6.13&#949;)</span>
                </p>
              </td>
</tr>
</tbody>
</table></div>
</div>
<br class="table-break"><div class="table">
<a name="math_toolkit.logs_and_tables.all_table.table_cyl_bessel_k"></a><p class="title"><b>Table&#160;23.18.&#160;Error rates for cyl_bessel_k</b></p>
<div class="table-contents"><table class="table" summary="Error rates for cyl_bessel_k">
<colgroup>
<col>
<col>
<col>
<col>
<col>
</colgroup>
<thead><tr>
<th>
              </th>
<th>
                <p>
                  GNU C++ version 7.1.0<br> linux<br> long double
                </p>
              </th>
<th>
                <p>
                  GNU C++ version 7.1.0<br> linux<br> double
                </p>
              </th>
<th>
                <p>
                  Sun compiler version 0x5150<br> Sun Solaris<br> long double
                </p>
              </th>
<th>
                <p>
                  Microsoft Visual C++ version 14.1<br> Win32<br> double
                </p>
              </th>
</tr></thead>
<tbody>
<tr>
<td>
                <p>
                  Bessel K0: Mathworld Data
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 0.833&#949; (Mean = 0.436&#949;)</span><br> <br>
                  (<span class="emphasis"><em>&lt;cmath&gt;:</em></span> Max = 9.33&#949; (Mean = 3.25&#949;))
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
                  2.1:</em></span> Max = 6.04&#949; (Mean = 2.16&#949;))<br> (<span class="emphasis"><em>Rmath
                  3.2.3:</em></span> Max = 0.833&#949; (Mean = 0.601&#949;))
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 0.833&#949; (Mean = 0.436&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 0.833&#949; (Mean = 0.552&#949;)</span>
                </p>
              </td>
</tr>
<tr>
<td>
                <p>
                  Bessel K1: Mathworld Data
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 0.786&#949; (Mean = 0.329&#949;)</span><br> <br>
                  (<span class="emphasis"><em>&lt;cmath&gt;:</em></span> Max = 8.94&#949; (Mean = 3.19&#949;))
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
                  2.1:</em></span> Max = 6.26&#949; (Mean = 2.21&#949;))<br> (<span class="emphasis"><em>Rmath
                  3.2.3:</em></span> Max = 0.894&#949; (Mean = 0.516&#949;))
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 0.786&#949; (Mean = 0.329&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 0.786&#949; (Mean = 0.39&#949;)</span>
                </p>
              </td>
</tr>
<tr>
<td>
                <p>
                  Bessel Kn: Mathworld Data
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 2.6&#949; (Mean = 1.21&#949;)</span><br> <br>
                  (<span class="emphasis"><em>&lt;cmath&gt;:</em></span> Max = 12.9&#949; (Mean = 4.91&#949;) <a class="link" href="logs.html#errors_GNU_C_version_7_1_0_linux_long_double_cyl_bessel_k__cmath__Bessel_Kn_Mathworld_Data">And
                  other failures.</a>)
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
                  2.1:</em></span> Max = 3.36&#949; (Mean = 1.43&#949;) <a class="link" href="logs.html#errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_k_GSL_2_1_Bessel_Kn_Mathworld_Data">And
                  other failures.</a>)<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span>
                  Max = 8.48&#949; (Mean = 2.98&#949;))
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 2.6&#949; (Mean = 1.21&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 3.63&#949; (Mean = 1.46&#949;)</span>
                </p>
              </td>
</tr>
<tr>
<td>
                <p>
                  Bessel Kv: Mathworld Data
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 3.58&#949; (Mean = 2.39&#949;)</span><br> <br>
                  (<span class="emphasis"><em>&lt;cmath&gt;:</em></span> Max = 13&#949; (Mean = 4.81&#949;) <a class="link" href="logs.html#errors_GNU_C_version_7_1_0_linux_long_double_cyl_bessel_k__cmath__Bessel_Kv_Mathworld_Data">And
                  other failures.</a>)
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
                  2.1:</em></span> Max = 5.47&#949; (Mean = 2.04&#949;) <a class="link" href="logs.html#errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_k_GSL_2_1_Bessel_Kv_Mathworld_Data">And
                  other failures.</a>)<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span>
                  Max = 3.15&#949; (Mean = 1.35&#949;))
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 5.21&#949; (Mean = 2.53&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 4.78&#949; (Mean = 2.19&#949;)</span>
                </p>
              </td>
</tr>
<tr>
<td>
                <p>
                  Bessel Kv: Mathworld Data (large values)
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 42.3&#949; (Mean = 21&#949;)</span><br> <br>
                  (<span class="emphasis"><em>&lt;cmath&gt;:</em></span> Max = 42.3&#949; (Mean = 19.8&#949;) <a class="link" href="logs.html#errors_GNU_C_version_7_1_0_linux_long_double_cyl_bessel_k__cmath__Bessel_Kv_Mathworld_Data_large_values_">And
                  other failures.</a>)
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
                  2.1:</em></span> Max = 308&#949; (Mean = 142&#949;) <a class="link" href="logs.html#errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_k_GSL_2_1_Bessel_Kv_Mathworld_Data_large_values_">And
                  other failures.</a>)<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span>
                  Max = 84.6&#949; (Mean = 37.8&#949;))
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 42.3&#949; (Mean = 21&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 59.8&#949; (Mean = 26.9&#949;)</span>
                </p>
              </td>
</tr>
<tr>
<td>
                <p>
                  Bessel Kn: Random Data
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 4.55&#949; (Mean = 1.12&#949;)</span><br> <br>
                  (<span class="emphasis"><em>&lt;cmath&gt;:</em></span> Max = 13.9&#949; (Mean = 2.91&#949;))
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 0.764&#949; (Mean = 0.0348&#949;)</span><br>
                  <br> (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 8.71&#949; (Mean = 1.76&#949;)
                  <a class="link" href="logs.html#errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_k_GSL_2_1_Bessel_Kn_Random_Data">And
                  other failures.</a>)<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span>
                  Max = 7.47&#949; (Mean = 1.34&#949;))
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 4.55&#949; (Mean = 1.12&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 9.34&#949; (Mean = 1.7&#949;)</span>
                </p>
              </td>
</tr>
<tr>
<td>
                <p>
                  Bessel Kv: Random Data
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 7.88&#949; (Mean = 1.48&#949;)</span><br> <br>
                  (<span class="emphasis"><em>&lt;cmath&gt;:</em></span> Max = 13.6&#949; (Mean = 2.68&#949;) <a class="link" href="logs.html#errors_GNU_C_version_7_1_0_linux_long_double_cyl_bessel_k__cmath__Bessel_Kv_Random_Data">And
                  other failures.</a>)
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 0.507&#949; (Mean = 0.0313&#949;)</span><br>
                  <br> (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 9.71&#949; (Mean = 1.47&#949;)
                  <a class="link" href="logs.html#errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_k_GSL_2_1_Bessel_Kv_Random_Data">And
                  other failures.</a>)<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span>
                  Max = 7.37&#949; (Mean = 1.49&#949;))
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 7.88&#949; (Mean = 1.47&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 8.33&#949; (Mean = 1.62&#949;)</span>
                </p>
              </td>
</tr>
</tbody>
</table></div>
</div>
<br class="table-break"><div class="table">
<a name="math_toolkit.logs_and_tables.all_table.table_cyl_bessel_k_integer_orders_"></a><p class="title"><b>Table&#160;23.19.&#160;Error rates for cyl_bessel_k (integer orders)</b></p>
<div class="table-contents"><table class="table" summary="Error rates for cyl_bessel_k (integer orders)">
<colgroup>
<col>
<col>
<col>
<col>
<col>
</colgroup>
<thead><tr>
<th>
              </th>
<th>
                <p>
                  GNU C++ version 7.1.0<br> linux<br> long double
                </p>
              </th>
<th>
                <p>
                  GNU C++ version 7.1.0<br> linux<br> double
                </p>
              </th>
<th>
                <p>
                  Sun compiler version 0x5150<br> Sun Solaris<br> long double
                </p>
              </th>
<th>
                <p>
                  Microsoft Visual C++ version 14.1<br> Win32<br> double
                </p>
              </th>
</tr></thead>
<tbody>
<tr>
<td>
                <p>
                  Bessel K0: Mathworld Data (Integer Version)
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 0.833&#949; (Mean = 0.436&#949;)</span><br> <br>
                  (<span class="emphasis"><em>&lt;cmath&gt;:</em></span> Max = 9.33&#949; (Mean = 3.25&#949;))
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
                  2.1:</em></span> Max = 1.2&#949; (Mean = 0.733&#949;))<br> (<span class="emphasis"><em>Rmath
                  3.2.3:</em></span> Max = 0.833&#949; (Mean = 0.601&#949;))
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 0.833&#949; (Mean = 0.436&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 0.833&#949; (Mean = 0.552&#949;)</span>
                </p>
              </td>
</tr>
<tr>
<td>
                <p>
                  Bessel K1: Mathworld Data (Integer Version)
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 0.786&#949; (Mean = 0.329&#949;)</span><br> <br>
                  (<span class="emphasis"><em>&lt;cmath&gt;:</em></span> Max = 8.94&#949; (Mean = 3.19&#949;))
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
                  2.1:</em></span> Max = 0.626&#949; (Mean = 0.333&#949;))<br> (<span class="emphasis"><em>Rmath
                  3.2.3:</em></span> Max = 0.894&#949; (Mean = 0.516&#949;))
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 0.786&#949; (Mean = 0.329&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 0.786&#949; (Mean = 0.39&#949;)</span>
                </p>
              </td>
</tr>
<tr>
<td>
                <p>
                  Bessel Kn: Mathworld Data (Integer Version)
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 2.6&#949; (Mean = 1.21&#949;)</span><br> <br>
                  (<span class="emphasis"><em>&lt;cmath&gt;:</em></span> Max = 12.9&#949; (Mean = 4.91&#949;) <a class="link" href="logs.html#errors_GNU_C_version_7_1_0_linux_long_double_cyl_bessel_k_integer_orders___cmath__Bessel_Kn_Mathworld_Data_Integer_Version_">And
                  other failures.</a>)
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
                  2.1:</em></span> Max = 168&#949; (Mean = 59.5&#949;))<br> (<span class="emphasis"><em>Rmath
                  3.2.3:</em></span> Max = 8.48&#949; (Mean = 2.98&#949;))
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 2.6&#949; (Mean = 1.21&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 3.63&#949; (Mean = 1.46&#949;)</span>
                </p>
              </td>
</tr>
</tbody>
</table></div>
</div>
<br class="table-break"><div class="table">
<a name="math_toolkit.logs_and_tables.all_table.table_cyl_bessel_k_prime"></a><p class="title"><b>Table&#160;23.20.&#160;Error rates for cyl_bessel_k_prime</b></p>
<div class="table-contents"><table class="table" summary="Error rates for cyl_bessel_k_prime">
<colgroup>
<col>
<col>
<col>
<col>
<col>
</colgroup>
<thead><tr>
<th>
              </th>
<th>
                <p>
                  GNU C++ version 7.1.0<br> linux<br> double
                </p>
              </th>
<th>
                <p>
                  GNU C++ version 7.1.0<br> linux<br> long double
                </p>
              </th>
<th>
                <p>
                  Sun compiler version 0x5150<br> Sun Solaris<br> long double
                </p>
              </th>
<th>
                <p>
                  Microsoft Visual C++ version 14.1<br> Win32<br> double
                </p>
              </th>
</tr></thead>
<tbody>
<tr>
<td>
                <p>
                  Bessel K'0: Mathworld Data
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 0.786&#949; (Mean = 0.329&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 0.786&#949; (Mean = 0.329&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 0.786&#949; (Mean = 0.39&#949;)</span>
                </p>
              </td>
</tr>
<tr>
<td>
                <p>
                  Bessel K'1: Mathworld Data
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 0.736&#949; (Mean = 0.389&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 0.736&#949; (Mean = 0.389&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 0.761&#949; (Mean = 0.444&#949;)</span>
                </p>
              </td>
</tr>
<tr>
<td>
                <p>
                  Bessel K'n: Mathworld Data
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 2.16&#949; (Mean = 1.08&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 2.16&#949; (Mean = 1.08&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 4.17&#949; (Mean = 1.75&#949;)</span>
                </p>
              </td>
</tr>
<tr>
<td>
                <p>
                  Bessel K'v: Mathworld Data
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 3.94&#949; (Mean = 2.44&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 3.94&#949; (Mean = 2.34&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 3.94&#949; (Mean = 1.47&#949;)</span>
                </p>
              </td>
</tr>
<tr>
<td>
                <p>
                  Bessel K'v: Mathworld Data (large values)
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 59.2&#949; (Mean = 42.9&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 58.7&#949; (Mean = 42.6&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 18.6&#949; (Mean = 11.8&#949;)</span>
                </p>
              </td>
</tr>
<tr>
<td>
                <p>
                  Bessel K'n: Random Data
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 4.45&#949; (Mean = 1.19&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 4.45&#949; (Mean = 1.19&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 9.67&#949; (Mean = 1.73&#949;)</span>
                </p>
              </td>
</tr>
<tr>
<td>
                <p>
                  Bessel K'v: Random Data
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 7.95&#949; (Mean = 1.53&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 7.95&#949; (Mean = 1.52&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 8.32&#949; (Mean = 1.65&#949;)</span>
                </p>
              </td>
</tr>
</tbody>
</table></div>
</div>
<br class="table-break"><div class="table">
<a name="math_toolkit.logs_and_tables.all_table.table_cyl_bessel_k_prime_integer_orders_"></a><p class="title"><b>Table&#160;23.21.&#160;Error rates for cyl_bessel_k_prime (integer orders)</b></p>
<div class="table-contents"><table class="table" summary="Error rates for cyl_bessel_k_prime (integer orders)">
<colgroup>
<col>
<col>
<col>
<col>
<col>
</colgroup>
<thead><tr>
<th>
              </th>
<th>
                <p>
                  GNU C++ version 7.1.0<br> linux<br> double
                </p>
              </th>
<th>
                <p>
                  GNU C++ version 7.1.0<br> linux<br> long double
                </p>
              </th>
<th>
                <p>
                  Sun compiler version 0x5150<br> Sun Solaris<br> long double
                </p>
              </th>
<th>
                <p>
                  Microsoft Visual C++ version 14.1<br> Win32<br> double
                </p>
              </th>
</tr></thead>
<tbody>
<tr>
<td>
                <p>
                  Bessel K'0: Mathworld Data (Integer Version)
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 0.786&#949; (Mean = 0.329&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 0.786&#949; (Mean = 0.329&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 0.786&#949; (Mean = 0.39&#949;)</span>
                </p>
              </td>
</tr>
<tr>
<td>
                <p>
                  Bessel K'1: Mathworld Data (Integer Version)
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 0.736&#949; (Mean = 0.389&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 0.736&#949; (Mean = 0.389&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 0.761&#949; (Mean = 0.444&#949;)</span>
                </p>
              </td>
</tr>
<tr>
<td>
                <p>
                  Bessel K'n: Mathworld Data (Integer Version)
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 2.16&#949; (Mean = 1.08&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 2.16&#949; (Mean = 1.08&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 4.17&#949; (Mean = 1.75&#949;)</span>
                </p>
              </td>
</tr>
</tbody>
</table></div>
</div>
<br class="table-break"><div class="table">
<a name="math_toolkit.logs_and_tables.all_table.table_cyl_neumann"></a><p class="title"><b>Table&#160;23.22.&#160;Error rates for cyl_neumann</b></p>
<div class="table-contents"><table class="table" summary="Error rates for cyl_neumann">
<colgroup>
<col>
<col>
<col>
<col>
<col>
</colgroup>
<thead><tr>
<th>
              </th>
<th>
                <p>
                  GNU C++ version 7.1.0<br> linux<br> long double
                </p>
              </th>
<th>
                <p>
                  GNU C++ version 7.1.0<br> linux<br> double
                </p>
              </th>
<th>
                <p>
                  Sun compiler version 0x5150<br> Sun Solaris<br> long double
                </p>
              </th>
<th>
                <p>
                  Microsoft Visual C++ version 14.1<br> Win32<br> double
                </p>
              </th>
</tr></thead>
<tbody>
<tr>
<td>
                <p>
                  Y0: Mathworld Data
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 5.53&#949; (Mean = 2.4&#949;)</span><br> <br>
                  (<span class="emphasis"><em>&lt;cmath&gt;:</em></span> Max = 2.05e+05&#949; (Mean = 6.87e+04&#949;))
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
                  2.1:</em></span> Max = 60.9&#949; (Mean = 20.4&#949;))<br> (<span class="emphasis"><em>Rmath
                  3.2.3:</em></span> Max = 167&#949; (Mean = 56.5&#949;))
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 5.53&#949; (Mean = 2.4&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 4.61&#949; (Mean = 2.29&#949;)</span>
                </p>
              </td>
</tr>
<tr>
<td>
                <p>
                  Y1: Mathworld Data
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 6.33&#949; (Mean = 2.25&#949;)</span><br> <br>
                  (<span class="emphasis"><em>&lt;cmath&gt;:</em></span> Max = 9.71e+03&#949; (Mean = 4.08e+03&#949;))
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
                  2.1:</em></span> Max = 23.4&#949; (Mean = 8.1&#949;))<br> (<span class="emphasis"><em>Rmath
                  3.2.3:</em></span> Max = 193&#949; (Mean = 64.4&#949;))
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 6.33&#949; (Mean = 2.29&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 4.75&#949; (Mean = 1.72&#949;)</span>
                </p>
              </td>
</tr>
<tr>
<td>
                <p>
                  Yn: Mathworld Data
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 55.2&#949; (Mean = 17.8&#949;)</span><br> <br>
                  (<span class="emphasis"><em>&lt;cmath&gt;:</em></span> <span class="red">Max = 2.2e+20&#949; (Mean
                  = 6.97e+19&#949;) <a class="link" href="logs.html#errors_GNU_C_version_7_1_0_linux_long_double_cyl_neumann__cmath__Yn_Mathworld_Data">And
                  other failures.</a>)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 0.993&#949; (Mean = 0.314&#949;)</span><br> <br>
                  (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 2.41e+05&#949; (Mean = 7.62e+04&#949;)
                  <a class="link" href="logs.html#errors_GNU_C_version_7_1_0_linux_double_cyl_neumann_GSL_2_1_Yn_Mathworld_Data">And
                  other failures.</a>)<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span>
                  Max = 1.24e+04&#949; (Mean = 4e+03&#949;))
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 55.2&#949; (Mean = 17.8&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 35&#949; (Mean = 11.9&#949;)</span>
                </p>
              </td>
</tr>
<tr>
<td>
                <p>
                  Yv: Mathworld Data
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 10.7&#949; (Mean = 4.93&#949;)</span><br> <br>
                  (<span class="emphasis"><em>&lt;cmath&gt;:</em></span> <span class="red">Max = 3.49e+15&#949; (Mean
                  = 1.05e+15&#949;) <a class="link" href="logs.html#errors_GNU_C_version_7_1_0_linux_long_double_cyl_neumann__cmath__Yv_Mathworld_Data">And
                  other failures.</a>)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 10&#949; (Mean = 3.02&#949;)</span><br> <br>
                  (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 1.07e+05&#949; (Mean = 3.22e+04&#949;)
                  <a class="link" href="logs.html#errors_GNU_C_version_7_1_0_linux_double_cyl_neumann_GSL_2_1_Yv_Mathworld_Data">And
                  other failures.</a>)<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span>
                  Max = 243&#949; (Mean = 73.9&#949;))
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 10.7&#949; (Mean = 5.1&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 7.89&#949; (Mean = 3.27&#949;)</span>
                </p>
              </td>
</tr>
<tr>
<td>
                <p>
                  Yv: Mathworld Data (large values)
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 1.7&#949; (Mean = 1.33&#949;)</span><br> <br>
                  (<span class="emphasis"><em>&lt;cmath&gt;:</em></span> Max = 43.2&#949; (Mean = 16.3&#949;) <a class="link" href="logs.html#errors_GNU_C_version_7_1_0_linux_long_double_cyl_neumann__cmath__Yv_Mathworld_Data_large_values_">And
                  other failures.</a>)
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
                  2.1:</em></span> Max = 60.8&#949; (Mean = 23&#949;) <a class="link" href="logs.html#errors_GNU_C_version_7_1_0_linux_double_cyl_neumann_GSL_2_1_Yv_Mathworld_Data_large_values_">And
                  other failures.</a>)<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span>
                  Max = 0.682&#949; (Mean = 0.335&#949;))
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 1.7&#949; (Mean = 1.33&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 0.682&#949; (Mean = 0.423&#949;)</span>
                </p>
              </td>
</tr>
<tr>
<td>
                <p>
                  Y0 and Y1: Random Data
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 10.8&#949; (Mean = 3.04&#949;)</span><br> <br>
                  (<span class="emphasis"><em>&lt;cmath&gt;:</em></span> Max = 2.59e+03&#949; (Mean = 500&#949;))
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
                  2.1:</em></span> Max = 34.4&#949; (Mean = 8.9&#949;))<br> (<span class="emphasis"><em>Rmath
                  3.2.3:</em></span> Max = 83&#949; (Mean = 14.2&#949;))
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 10.8&#949; (Mean = 3.04&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 4.17&#949; (Mean = 1.24&#949;)</span>
                </p>
              </td>
</tr>
<tr>
<td>
                <p>
                  Yn: Random Data
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 338&#949; (Mean = 27.5&#949;)</span><br> <br>
                  (<span class="emphasis"><em>&lt;cmath&gt;:</em></span> Max = 4.01e+03&#949; (Mean = 348&#949;))
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
                  2.1:</em></span> Max = 500&#949; (Mean = 47.8&#949;))<br> (<span class="emphasis"><em>Rmath
                  3.2.3:</em></span> Max = 691&#949; (Mean = 67.9&#949;))
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 338&#949; (Mean = 27.5&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 117&#949; (Mean = 10.2&#949;)</span>
                </p>
              </td>
</tr>
<tr>
<td>
                <p>
                  Yv: Random Data
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 2.08e+03&#949; (Mean = 149&#949;)</span><br>
                  <br> (<span class="emphasis"><em>&lt;cmath&gt;:</em></span> <span class="red">Max
                  = +INF&#949; (Mean = +INF&#949;) <a class="link" href="logs.html#errors_GNU_C_version_7_1_0_linux_long_double_cyl_neumann__cmath__Yv_Random_Data">And
                  other failures.</a>)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 1.53&#949; (Mean = 0.102&#949;)</span><br> <br>
                  (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 1.41e+06&#949; (Mean = 7.67e+04&#949;))<br>
                  (<span class="emphasis"><em>Rmath 3.2.3:</em></span> Max = 1.79e+05&#949; (Mean = 9.64e+03&#949;))
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 2.08e+03&#949; (Mean = 149&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 1.23e+03&#949; (Mean = 69.9&#949;)</span>
                </p>
              </td>
</tr>
</tbody>
</table></div>
</div>
<br class="table-break"><div class="table">
<a name="math_toolkit.logs_and_tables.all_table.table_cyl_neumann_integer_orders_"></a><p class="title"><b>Table&#160;23.23.&#160;Error rates for cyl_neumann (integer orders)</b></p>
<div class="table-contents"><table class="table" summary="Error rates for cyl_neumann (integer orders)">
<colgroup>
<col>
<col>
<col>
<col>
<col>
</colgroup>
<thead><tr>
<th>
              </th>
<th>
                <p>
                  GNU C++ version 7.1.0<br> linux<br> long double
                </p>
              </th>
<th>
                <p>
                  GNU C++ version 7.1.0<br> linux<br> double
                </p>
              </th>
<th>
                <p>
                  Sun compiler version 0x5150<br> Sun Solaris<br> long double
                </p>
              </th>
<th>
                <p>
                  Microsoft Visual C++ version 14.1<br> Win32<br> double
                </p>
              </th>
</tr></thead>
<tbody>
<tr>
<td>
                <p>
                  Y0: Mathworld Data (Integer Version)
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 5.53&#949; (Mean = 2.4&#949;)</span><br> <br>
                  (<span class="emphasis"><em>&lt;cmath&gt;:</em></span> Max = 2.05e+05&#949; (Mean = 6.87e+04&#949;))
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
                  2.1:</em></span> Max = 6.46&#949; (Mean = 2.38&#949;))<br> (<span class="emphasis"><em>Rmath
                  3.2.3:</em></span> Max = 167&#949; (Mean = 56.5&#949;))
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 5.53&#949; (Mean = 2.4&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 4.61&#949; (Mean = 2.29&#949;)</span><br> <br>
                  (<span class="emphasis"><em>&lt;math.h&gt;:</em></span> Max = 5.37e+03&#949; (Mean = 1.81e+03&#949;))
                </p>
              </td>
</tr>
<tr>
<td>
                <p>
                  Y1: Mathworld Data (Integer Version)
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 6.33&#949; (Mean = 2.25&#949;)</span><br> <br>
                  (<span class="emphasis"><em>&lt;cmath&gt;:</em></span> Max = 9.71e+03&#949; (Mean = 4.08e+03&#949;))
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
                  2.1:</em></span> Max = 1.51&#949; (Mean = 0.839&#949;))<br> (<span class="emphasis"><em>Rmath
                  3.2.3:</em></span> Max = 193&#949; (Mean = 64.4&#949;))
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 6.33&#949; (Mean = 2.29&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 4.75&#949; (Mean = 1.72&#949;)</span><br> <br>
                  (<span class="emphasis"><em>&lt;math.h&gt;:</em></span> Max = 1.86e+04&#949; (Mean = 6.2e+03&#949;))
                </p>
              </td>
</tr>
<tr>
<td>
                <p>
                  Yn: Mathworld Data (Integer Version)
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 55.2&#949; (Mean = 17.8&#949;)</span><br> <br>
                  (<span class="emphasis"><em>&lt;cmath&gt;:</em></span> <span class="red">Max = 2.2e+20&#949; (Mean
                  = 6.97e+19&#949;) <a class="link" href="logs.html#errors_GNU_C_version_7_1_0_linux_long_double_cyl_neumann_integer_orders___cmath__Yn_Mathworld_Data_Integer_Version_">And
                  other failures.</a>)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 0.993&#949; (Mean = 0.314&#949;)</span><br> <br>
                  (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 2.41e+05&#949; (Mean = 7.62e+04&#949;))<br>
                  (<span class="emphasis"><em>Rmath 3.2.3:</em></span> Max = 1.24e+04&#949; (Mean = 4e+03&#949;))
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 55.2&#949; (Mean = 17.8&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 35&#949; (Mean = 11.9&#949;)</span><br> <br>
                  (<span class="emphasis"><em>&lt;math.h&gt;:</em></span> Max = 2.49e+05&#949; (Mean = 8.14e+04&#949;))
                </p>
              </td>
</tr>
</tbody>
</table></div>
</div>
<br class="table-break"><div class="table">
<a name="math_toolkit.logs_and_tables.all_table.table_cyl_neumann_prime"></a><p class="title"><b>Table&#160;23.24.&#160;Error rates for cyl_neumann_prime</b></p>
<div class="table-contents"><table class="table" summary="Error rates for cyl_neumann_prime">
<colgroup>
<col>
<col>
<col>
<col>
<col>
</colgroup>
<thead><tr>
<th>
              </th>
<th>
                <p>
                  GNU C++ version 7.1.0<br> linux<br> double
                </p>
              </th>
<th>
                <p>
                  GNU C++ version 7.1.0<br> linux<br> long double
                </p>
              </th>
<th>
                <p>
                  Sun compiler version 0x5150<br> Sun Solaris<br> long double
                </p>
              </th>
<th>
                <p>
                  Microsoft Visual C++ version 14.1<br> Win32<br> double
                </p>
              </th>
</tr></thead>
<tbody>
<tr>
<td>
                <p>
                  Y'0: Mathworld Data
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 6.33&#949; (Mean = 3.12&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 6.33&#949; (Mean = 3.14&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 4.75&#949; (Mean = 1.75&#949;)</span>
                </p>
              </td>
</tr>
<tr>
<td>
                <p>
                  Y'1: Mathworld Data
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 0.58&#949; (Mean = 0.193&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 37.1&#949; (Mean = 12.8&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 34&#949; (Mean = 11.8&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 3.08&#949; (Mean = 1.2&#949;)</span>
                </p>
              </td>
</tr>
<tr>
<td>
                <p>
                  Y'n: Mathworld Data
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 2.05&#949; (Mean = 0.677&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 56&#949; (Mean = 18.2&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 56&#949; (Mean = 21.3&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 563&#949; (Mean = 178&#949;)</span>
                </p>
              </td>
</tr>
<tr>
<td>
                <p>
                  Y'v: Mathworld Data
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 21.5&#949; (Mean = 6.49&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 42.5&#949; (Mean = 13.4&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 42.5&#949; (Mean = 13.6&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 23.7&#949; (Mean = 10.1&#949;)</span>
                </p>
              </td>
</tr>
<tr>
<td>
                <p>
                  Y'v: Mathworld Data (large values)
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 1.57&#949; (Mean = 1.24&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 1.57&#949; (Mean = 1.24&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 0.627&#949; (Mean = 0.237&#949;)</span>
                </p>
              </td>
</tr>
<tr>
<td>
                <p>
                  Y'0 and Y'1: Random Data
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 23.8&#949; (Mean = 3.69&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 23.8&#949; (Mean = 3.69&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 5.95&#949; (Mean = 1.36&#949;)</span>
                </p>
              </td>
</tr>
<tr>
<td>
                <p>
                  Y'n: Random Data
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 1.53&#949; (Mean = 0.0885&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 2.35e+03&#949; (Mean = 136&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 2.35e+03&#949; (Mean = 136&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 621&#949; (Mean = 36&#949;)</span>
                </p>
              </td>
</tr>
<tr>
<td>
                <p>
                  Y'v: Random Data
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 56.8&#949; (Mean = 2.59&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 1.16e+05&#949; (Mean = 5.28e+03&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 1.16e+05&#949; (Mean = 5.28e+03&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 3.23e+04&#949; (Mean = 1.13e+03&#949;)</span>
                </p>
              </td>
</tr>
</tbody>
</table></div>
</div>
<br class="table-break"><div class="table">
<a name="math_toolkit.logs_and_tables.all_table.table_cyl_neumann_prime_integer_orders_"></a><p class="title"><b>Table&#160;23.25.&#160;Error rates for cyl_neumann_prime (integer orders)</b></p>
<div class="table-contents"><table class="table" summary="Error rates for cyl_neumann_prime (integer orders)">
<colgroup>
<col>
<col>
<col>
<col>
<col>
</colgroup>
<thead><tr>
<th>
              </th>
<th>
                <p>
                  GNU C++ version 7.1.0<br> linux<br> double
                </p>
              </th>
<th>
                <p>
                  GNU C++ version 7.1.0<br> linux<br> long double
                </p>
              </th>
<th>
                <p>
                  Sun compiler version 0x5150<br> Sun Solaris<br> long double
                </p>
              </th>
<th>
                <p>
                  Microsoft Visual C++ version 14.1<br> Win32<br> double
                </p>
              </th>
</tr></thead>
<tbody>
<tr>
<td>
                <p>
                  Y'0: Mathworld Data (Integer Version)
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 6.33&#949; (Mean = 3.12&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 6.33&#949; (Mean = 3.14&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 4.75&#949; (Mean = 1.75&#949;)</span>
                </p>
              </td>
</tr>
<tr>
<td>
                <p>
                  Y'1: Mathworld Data (Integer Version)
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 0.58&#949; (Mean = 0.193&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 37.1&#949; (Mean = 12.8&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 34&#949; (Mean = 11.8&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 3.08&#949; (Mean = 1.2&#949;)</span>
                </p>
              </td>
</tr>
<tr>
<td>
                <p>
                  Y'n: Mathworld Data (Integer Version)
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 2.05&#949; (Mean = 0.677&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 56&#949; (Mean = 18.2&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 56&#949; (Mean = 21.3&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 563&#949; (Mean = 178&#949;)</span>
                </p>
              </td>
</tr>
</tbody>
</table></div>
</div>
<br class="table-break"><div class="table">
<a name="math_toolkit.logs_and_tables.all_table.table_digamma"></a><p class="title"><b>Table&#160;23.26.&#160;Error rates for digamma</b></p>
<div class="table-contents"><table class="table" summary="Error rates for digamma">
<colgroup>
<col>
<col>
<col>
<col>
<col>
</colgroup>
<thead><tr>
<th>
              </th>
<th>
                <p>
                  GNU C++ version 7.1.0<br> linux<br> double
                </p>
              </th>
<th>
                <p>
                  GNU C++ version 7.1.0<br> linux<br> long double
                </p>
              </th>
<th>
                <p>
                  Sun compiler version 0x5150<br> Sun Solaris<br> long double
                </p>
              </th>
<th>
                <p>
                  Microsoft Visual C++ version 14.1<br> Win32<br> double
                </p>
              </th>
</tr></thead>
<tbody>
<tr>
<td>
                <p>
                  Digamma Function: Large Values
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
                  2.1:</em></span> Max = 1.84&#949; (Mean = 0.71&#949;))<br> (<span class="emphasis"><em>Rmath
                  3.2.3:</em></span> Max = 1.18&#949; (Mean = 0.331&#949;))
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 1.39&#949; (Mean = 0.413&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 1.39&#949; (Mean = 0.413&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 0.98&#949; (Mean = 0.369&#949;)</span>
                </p>
              </td>
</tr>
<tr>
<td>
                <p>
                  Digamma Function: Near the Positive Root
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 0.891&#949; (Mean = 0.0995&#949;)</span><br>
                  <br> (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 135&#949; (Mean = 11.9&#949;))<br>
                  (<span class="emphasis"><em>Rmath 3.2.3:</em></span> Max = 2.02e+03&#949; (Mean = 256&#949;))
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 1.37&#949; (Mean = 0.477&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 1.31&#949; (Mean = 0.471&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 0.997&#949; (Mean = 0.527&#949;)</span>
                </p>
              </td>
</tr>
<tr>
<td>
                <p>
                  Digamma Function: Near Zero
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
                  2.1:</em></span> Max = 0.953&#949; (Mean = 0.348&#949;))<br> (<span class="emphasis"><em>Rmath
                  3.2.3:</em></span> Max = 1.17&#949; (Mean = 0.564&#949;))
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 0.984&#949; (Mean = 0.361&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 0.984&#949; (Mean = 0.361&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 0.953&#949; (Mean = 0.337&#949;)</span>
                </p>
              </td>
</tr>
<tr>
<td>
                <p>
                  Digamma Function: Negative Values
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
                  2.1:</em></span> Max = 4.56e+04&#949; (Mean = 3.91e+03&#949;))<br> (<span class="emphasis"><em>Rmath
                  3.2.3:</em></span> Max = 4.6e+04&#949; (Mean = 3.94e+03&#949;))
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 180&#949; (Mean = 13&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 180&#949; (Mean = 13&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 214&#949; (Mean = 16.1&#949;)</span>
                </p>
              </td>
</tr>
<tr>
<td>
                <p>
                  Digamma Function: Values near 0
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
                  2.1:</em></span> Max = 0.866&#949; (Mean = 0.387&#949;))<br> (<span class="emphasis"><em>Rmath
                  3.2.3:</em></span> Max = 3.58e+05&#949; (Mean = 1.6e+05&#949;))
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 1&#949; (Mean = 0.592&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 1&#949; (Mean = 0.592&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span>
                </p>
              </td>
</tr>
<tr>
<td>
                <p>
                  Digamma Function: Integer arguments
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 0.992&#949; (Mean = 0.215&#949;)</span><br> <br>
                  (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 1.18&#949; (Mean = 0.607&#949;))<br>
                  (<span class="emphasis"><em>Rmath 3.2.3:</em></span> Max = 4.33&#949; (Mean = 0.982&#949;))
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 0.888&#949; (Mean = 0.403&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 0.888&#949; (Mean = 0.403&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 0.992&#949; (Mean = 0.452&#949;)</span>
                </p>
              </td>
</tr>
<tr>
<td>
                <p>
                  Digamma Function: Half integer arguments
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
                  2.1:</em></span> Max = 1.09&#949; (Mean = 0.531&#949;))<br> (<span class="emphasis"><em>Rmath
                  3.2.3:</em></span> Max = 46.2&#949; (Mean = 7.24&#949;))
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 0.906&#949; (Mean = 0.409&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 0.906&#949; (Mean = 0.409&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 0.78&#949; (Mean = 0.314&#949;)</span>
                </p>
              </td>
</tr>
</tbody>
</table></div>
</div>
<br class="table-break"><div class="table">
<a name="math_toolkit.logs_and_tables.all_table.table_ellint_1"></a><p class="title"><b>Table&#160;23.27.&#160;Error rates for ellint_1</b></p>
<div class="table-contents"><table class="table" summary="Error rates for ellint_1">
<colgroup>
<col>
<col>
<col>
<col>
<col>
</colgroup>
<thead><tr>
<th>
              </th>
<th>
                <p>
                  GNU C++ version 7.1.0<br> linux<br> long double
                </p>
              </th>
<th>
                <p>
                  GNU C++ version 7.1.0<br> linux<br> double
                </p>
              </th>
<th>
                <p>
                  Sun compiler version 0x5150<br> Sun Solaris<br> long double
                </p>
              </th>
<th>
                <p>
                  Microsoft Visual C++ version 14.1<br> Win32<br> double
                </p>
              </th>
</tr></thead>
<tbody>
<tr>
<td>
                <p>
                  Elliptic Integral F: Mathworld Data
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 0.94&#949; (Mean = 0.509&#949;)</span><br> <br>
                  (<span class="emphasis"><em>&lt;cmath&gt;:</em></span> <span class="red">Max = +INF&#949; (Mean
                  = +INF&#949;) <a class="link" href="logs.html#errors_GNU_C_version_7_1_0_linux_long_double_ellint_1__cmath__Elliptic_Integral_F_Mathworld_Data">And
                  other failures.</a>)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
                  2.1:</em></span> Max = 0.919&#949; (Mean = 0.544&#949;))
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 0.94&#949; (Mean = 0.509&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 0.919&#949; (Mean = 0.542&#949;)</span>
                </p>
              </td>
</tr>
<tr>
<td>
                <p>
                  Elliptic Integral F: Random Data
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 1.57&#949; (Mean = 0.56&#949;)</span><br> <br>
                  (<span class="emphasis"><em>&lt;cmath&gt;:</em></span> Max = 2.56&#949; (Mean = 0.816&#949;))
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
                  2.1:</em></span> Max = 2.99&#949; (Mean = 0.797&#949;))
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 1.57&#949; (Mean = 0.561&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 2.26&#949; (Mean = 0.631&#949;)</span>
                </p>
              </td>
</tr>
</tbody>
</table></div>
</div>
<br class="table-break"><div class="table">
<a name="math_toolkit.logs_and_tables.all_table.table_ellint_1_complete_"></a><p class="title"><b>Table&#160;23.28.&#160;Error rates for ellint_1 (complete)</b></p>
<div class="table-contents"><table class="table" summary="Error rates for ellint_1 (complete)">
<colgroup>
<col>
<col>
<col>
<col>
<col>
</colgroup>
<thead><tr>
<th>
              </th>
<th>
                <p>
                  GNU C++ version 7.1.0<br> linux<br> long double
                </p>
              </th>
<th>
                <p>
                  GNU C++ version 7.1.0<br> linux<br> double
                </p>
              </th>
<th>
                <p>
                  Sun compiler version 0x5150<br> Sun Solaris<br> long double
                </p>
              </th>
<th>
                <p>
                  Microsoft Visual C++ version 14.1<br> Win32<br> double
                </p>
              </th>
</tr></thead>
<tbody>
<tr>
<td>
                <p>
                  Elliptic Integral K: Mathworld Data
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 0.887&#949; (Mean = 0.296&#949;)</span><br> <br>
                  (<span class="emphasis"><em>&lt;cmath&gt;:</em></span> Max = 1.19&#949; (Mean = 0.765&#949;))
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
                  2.1:</em></span> Max = 0.623&#949; (Mean = 0.393&#949;))
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 0.887&#949; (Mean = 0.296&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 0.915&#949; (Mean = 0.547&#949;)</span>
                </p>
              </td>
</tr>
<tr>
<td>
                <p>
                  Elliptic Integral K: Random Data
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 1.27&#949; (Mean = 0.473&#949;)</span><br> <br>
                  (<span class="emphasis"><em>&lt;cmath&gt;:</em></span> Max = 2.19&#949; (Mean = 0.694&#949;))
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 0.851&#949; (Mean = 0.0851&#949;)</span><br>
                  <br> (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 2.32&#949; (Mean = 0.688&#949;))
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 1.27&#949; (Mean = 0.473&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 0.958&#949; (Mean = 0.408&#949;)</span>
                </p>
              </td>
</tr>
</tbody>
</table></div>
</div>
<br class="table-break"><div class="table">
<a name="math_toolkit.logs_and_tables.all_table.table_ellint_2"></a><p class="title"><b>Table&#160;23.29.&#160;Error rates for ellint_2</b></p>
<div class="table-contents"><table class="table" summary="Error rates for ellint_2">
<colgroup>
<col>
<col>
<col>
<col>
<col>
</colgroup>
<thead><tr>
<th>
              </th>
<th>
                <p>
                  GNU C++ version 7.1.0<br> linux<br> double
                </p>
              </th>
<th>
                <p>
                  GNU C++ version 7.1.0<br> linux<br> long double
                </p>
              </th>
<th>
                <p>
                  Sun compiler version 0x5150<br> Sun Solaris<br> long double
                </p>
              </th>
<th>
                <p>
                  Microsoft Visual C++ version 14.1<br> Win32<br> double
                </p>
              </th>
</tr></thead>
<tbody>
<tr>
<td>
                <p>
                  Elliptic Integral E: Mathworld Data
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
                  2.1:</em></span> Max = 0.63&#949; (Mean = 0.325&#949;))
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 0.656&#949; (Mean = 0.317&#949;)</span><br> <br>
                  (<span class="emphasis"><em>&lt;cmath&gt;:</em></span> <span class="red">Max = +INF&#949; (Mean
                  = +INF&#949;) <a class="link" href="logs.html#errors_GNU_C_version_7_1_0_linux_long_double_ellint_2__cmath__Elliptic_Integral_E_Mathworld_Data">And
                  other failures.</a>)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 0.656&#949; (Mean = 0.317&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 1.31&#949; (Mean = 0.727&#949;)</span>
                </p>
              </td>
</tr>
<tr>
<td>
                <p>
                  Elliptic Integral E: Random Data
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
                  2.1:</em></span> Max = 4.4&#949; (Mean = 1.16&#949;))
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 2.05&#949; (Mean = 0.632&#949;)</span><br> <br>
                  (<span class="emphasis"><em>&lt;cmath&gt;:</em></span> Max = 3.08e+04&#949; (Mean = 3.84e+03&#949;))
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 2.05&#949; (Mean = 0.632&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 2.23&#949; (Mean = 0.639&#949;)</span>
                </p>
              </td>
</tr>
<tr>
<td>
                <p>
                  Elliptic Integral E: Small Angles
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
                  2.1:</em></span> Max = 0.5&#949; (Mean = 0.118&#949;))
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 1&#949; (Mean = 0.283&#949;)</span><br> <br>
                  (<span class="emphasis"><em>&lt;cmath&gt;:</em></span> Max = 2&#949; (Mean = 0.333&#949;))
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 1&#949; (Mean = 0.283&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 1&#949; (Mean = 0.421&#949;)</span>
                </p>
              </td>
</tr>
</tbody>
</table></div>
</div>
<br class="table-break"><div class="table">
<a name="math_toolkit.logs_and_tables.all_table.table_ellint_2_complete_"></a><p class="title"><b>Table&#160;23.30.&#160;Error rates for ellint_2 (complete)</b></p>
<div class="table-contents"><table class="table" summary="Error rates for ellint_2 (complete)">
<colgroup>
<col>
<col>
<col>
<col>
<col>
</colgroup>
<thead><tr>
<th>
              </th>
<th>
                <p>
                  GNU C++ version 7.1.0<br> linux<br> double
                </p>
              </th>
<th>
                <p>
                  GNU C++ version 7.1.0<br> linux<br> long double
                </p>
              </th>
<th>
                <p>
                  Sun compiler version 0x5150<br> Sun Solaris<br> long double
                </p>
              </th>
<th>
                <p>
                  Microsoft Visual C++ version 14.1<br> Win32<br> double
                </p>
              </th>
</tr></thead>
<tbody>
<tr>
<td>
                <p>
                  Elliptic Integral E: Mathworld Data
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
                  2.1:</em></span> Max = 3.09&#949; (Mean = 1.04&#949;) <a class="link" href="logs.html#errors_GNU_C_version_7_1_0_linux_double_ellint_2_complete__GSL_2_1_Elliptic_Integral_E_Mathworld_Data">And
                  other failures.</a>)
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 0.836&#949; (Mean = 0.469&#949;)</span><br> <br>
                  (<span class="emphasis"><em>&lt;cmath&gt;:</em></span> Max = 170&#949; (Mean = 55.1&#949;))
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 0.836&#949; (Mean = 0.469&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 1.3&#949; (Mean = 0.615&#949;)</span>
                </p>
              </td>
</tr>
<tr>
<td>
                <p>
                  Elliptic Integral E: Random Data
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
                  2.1:</em></span> Max = 4.34&#949; (Mean = 1.18&#949;))
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 1.97&#949; (Mean = 0.629&#949;)</span><br> <br>
                  (<span class="emphasis"><em>&lt;cmath&gt;:</em></span> Max = 2.49e+04&#949; (Mean = 3.39e+03&#949;))
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 1.97&#949; (Mean = 0.629&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 1.71&#949; (Mean = 0.553&#949;)</span>
                </p>
              </td>
</tr>
</tbody>
</table></div>
</div>
<br class="table-break"><div class="table">
<a name="math_toolkit.logs_and_tables.all_table.table_ellint_3"></a><p class="title"><b>Table&#160;23.31.&#160;Error rates for ellint_3</b></p>
<div class="table-contents"><table class="table" summary="Error rates for ellint_3">
<colgroup>
<col>
<col>
<col>
<col>
<col>
</colgroup>
<thead><tr>
<th>
              </th>
<th>
                <p>
                  GNU C++ version 7.1.0<br> linux<br> long double
                </p>
              </th>
<th>
                <p>
                  GNU C++ version 7.1.0<br> linux<br> double
                </p>
              </th>
<th>
                <p>
                  Sun compiler version 0x5150<br> Sun Solaris<br> long double
                </p>
              </th>
<th>
                <p>
                  Microsoft Visual C++ version 14.1<br> Win32<br> double
                </p>
              </th>
</tr></thead>
<tbody>
<tr>
<td>
                <p>
                  Elliptic Integral PI: Mathworld Data
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 475&#949; (Mean = 86.3&#949;)</span><br> <br>
                  (<span class="emphasis"><em>&lt;cmath&gt;:</em></span> <span class="red">Max = +INF&#949; (Mean
                  = +INF&#949;) <a class="link" href="logs.html#errors_GNU_C_version_7_1_0_linux_long_double_ellint_3__cmath__Elliptic_Integral_PI_Mathworld_Data">And
                  other failures.</a>)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
                  2.1:</em></span> Max = 1.48e+05&#949; (Mean = 2.54e+04&#949;) <a class="link" href="logs.html#errors_GNU_C_version_7_1_0_linux_double_ellint_3_GSL_2_1_Elliptic_Integral_PI_Mathworld_Data">And
                  other failures.</a>)
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 475&#949; (Mean = 86.3&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 565&#949; (Mean = 102&#949;)</span>
                </p>
              </td>
</tr>
<tr>
<td>
                <p>
                  Elliptic Integral PI: Random Data
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 4.54&#949; (Mean = 0.895&#949;)</span><br> <br>
                  (<span class="emphasis"><em>&lt;cmath&gt;:</em></span> <span class="red">Max = 3.37e+20&#949; (Mean
                  = 3.47e+19&#949;) <a class="link" href="logs.html#errors_GNU_C_version_7_1_0_linux_long_double_ellint_3__cmath__Elliptic_Integral_PI_Random_Data">And
                  other failures.</a>)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
                  2.1:</em></span> Max = 633&#949; (Mean = 50.1&#949;))
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 4.49&#949; (Mean = 0.885&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 8.33&#949; (Mean = 0.971&#949;)</span>
                </p>
              </td>
</tr>
<tr>
<td>
                <p>
                  Elliptic Integral PI: Large Random Data
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 3.7&#949; (Mean = 0.893&#949;)</span><br> <br>
                  (<span class="emphasis"><em>&lt;cmath&gt;:</em></span> <span class="red">Max = 2.52e+18&#949; (Mean
                  = 4.83e+17&#949;) <a class="link" href="logs.html#errors_GNU_C_version_7_1_0_linux_long_double_ellint_3__cmath__Elliptic_Integral_PI_Large_Random_Data">And
                  other failures.</a>)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 0.557&#949; (Mean = 0.0389&#949;)</span><br>
                  <br> (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 40.1&#949; (Mean = 7.77&#949;))
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 3.7&#949; (Mean = 0.892&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 2.86&#949; (Mean = 0.944&#949;)</span>
                </p>
              </td>
</tr>
</tbody>
</table></div>
</div>
<br class="table-break"><div class="table">
<a name="math_toolkit.logs_and_tables.all_table.table_ellint_3_complete_"></a><p class="title"><b>Table&#160;23.32.&#160;Error rates for ellint_3 (complete)</b></p>
<div class="table-contents"><table class="table" summary="Error rates for ellint_3 (complete)">
<colgroup>
<col>
<col>
<col>
<col>
<col>
</colgroup>
<thead><tr>
<th>
              </th>
<th>
                <p>
                  GNU C++ version 7.1.0<br> linux<br> long double
                </p>
              </th>
<th>
                <p>
                  GNU C++ version 7.1.0<br> linux<br> double
                </p>
              </th>
<th>
                <p>
                  Sun compiler version 0x5150<br> Sun Solaris<br> long double
                </p>
              </th>
<th>
                <p>
                  Microsoft Visual C++ version 14.1<br> Win32<br> double
                </p>
              </th>
</tr></thead>
<tbody>
<tr>
<td>
                <p>
                  Complete Elliptic Integral PI: Mathworld Data
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 1.4&#949; (Mean = 0.575&#949;)</span><br> <br>
                  (<span class="emphasis"><em>&lt;cmath&gt;:</em></span> <span class="red">Max = 6.31e+20&#949; (Mean
                  = 1.53e+20&#949;) <a class="link" href="logs.html#errors_GNU_C_version_7_1_0_linux_long_double_ellint_3_complete___cmath__Complete_Elliptic_Integral_PI_Mathworld_Data">And
                  other failures.</a>)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
                  2.1:</em></span> Max = 6.33e+04&#949; (Mean = 1.54e+04&#949;) <a class="link" href="logs.html#errors_GNU_C_version_7_1_0_linux_double_ellint_3_complete__GSL_2_1_Complete_Elliptic_Integral_PI_Mathworld_Data">And
                  other failures.</a>)
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 1.4&#949; (Mean = 0.575&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 0.971&#949; (Mean = 0.464&#949;)</span>
                </p>
              </td>
</tr>
<tr>
<td>
                <p>
                  Complete Elliptic Integral PI: Random Data
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 2.45&#949; (Mean = 0.696&#949;)</span><br> <br>
                  (<span class="emphasis"><em>&lt;cmath&gt;:</em></span> <span class="red">Max = 8.78e+20&#949; (Mean
                  = 1.02e+20&#949;) <a class="link" href="logs.html#errors_GNU_C_version_7_1_0_linux_long_double_ellint_3_complete___cmath__Complete_Elliptic_Integral_PI_Random_Data">And
                  other failures.</a>)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
                  2.1:</em></span> Max = 24&#949; (Mean = 2.99&#949;))
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 2.4&#949; (Mean = 0.677&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 2.46&#949; (Mean = 0.657&#949;)</span>
                </p>
              </td>
</tr>
</tbody>
</table></div>
</div>
<br class="table-break"><div class="table">
<a name="math_toolkit.logs_and_tables.all_table.table_ellint_d"></a><p class="title"><b>Table&#160;23.33.&#160;Error rates for ellint_d</b></p>
<div class="table-contents"><table class="table" summary="Error rates for ellint_d">
<colgroup>
<col>
<col>
<col>
<col>
<col>
</colgroup>
<thead><tr>
<th>
              </th>
<th>
                <p>
                  GNU C++ version 7.1.0<br> linux<br> double
                </p>
              </th>
<th>
                <p>
                  GNU C++ version 7.1.0<br> linux<br> long double
                </p>
              </th>
<th>
                <p>
                  Sun compiler version 0x5150<br> Sun Solaris<br> long double
                </p>
              </th>
<th>
                <p>
                  Microsoft Visual C++ version 14.1<br> Win32<br> double
                </p>
              </th>
</tr></thead>
<tbody>
<tr>
<td>
                <p>
                  Elliptic Integral E: Mathworld Data
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
                  2.1:</em></span> Max = 0.862&#949; (Mean = 0.568&#949;))
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 1.3&#949; (Mean = 0.813&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 1.3&#949; (Mean = 0.813&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 0.862&#949; (Mean = 0.457&#949;)</span>
                </p>
              </td>
</tr>
<tr>
<td>
                <p>
                  Elliptic Integral D: Random Data
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
                  2.1:</em></span> Max = 3.01&#949; (Mean = 0.928&#949;))
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 2.51&#949; (Mean = 0.883&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 2.51&#949; (Mean = 0.883&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 2.87&#949; (Mean = 0.805&#949;)</span>
                </p>
              </td>
</tr>
</tbody>
</table></div>
</div>
<br class="table-break"><div class="table">
<a name="math_toolkit.logs_and_tables.all_table.table_ellint_d_complete_"></a><p class="title"><b>Table&#160;23.34.&#160;Error rates for ellint_d (complete)</b></p>
<div class="table-contents"><table class="table" summary="Error rates for ellint_d (complete)">
<colgroup>
<col>
<col>
<col>
<col>
<col>
</colgroup>
<thead><tr>
<th>
              </th>
<th>
                <p>
                  GNU C++ version 7.1.0<br> linux<br> double
                </p>
              </th>
<th>
                <p>
                  GNU C++ version 7.1.0<br> linux<br> long double
                </p>
              </th>
<th>
                <p>
                  Sun compiler version 0x5150<br> Sun Solaris<br> long double
                </p>
              </th>
<th>
                <p>
                  Microsoft Visual C++ version 14.1<br> Win32<br> double
                </p>
              </th>
</tr></thead>
<tbody>
<tr>
<td>
                <p>
                  Elliptic Integral E: Mathworld Data
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 0.637&#949; (Mean = 0.368&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 1.27&#949; (Mean = 0.735&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 1.27&#949; (Mean = 0.735&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 0.637&#949; (Mean = 0.368&#949;)</span>
                </p>
              </td>
</tr>
<tr>
<td>
                <p>
                  Elliptic Integral D: Random Data
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 1.27&#949; (Mean = 0.334&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 1.27&#949; (Mean = 0.334&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 1.27&#949; (Mean = 0.355&#949;)</span>
                </p>
              </td>
</tr>
</tbody>
</table></div>
</div>
<br class="table-break"><div class="table">
<a name="math_toolkit.logs_and_tables.all_table.table_ellint_rc"></a><p class="title"><b>Table&#160;23.35.&#160;Error rates for ellint_rc</b></p>
<div class="table-contents"><table class="table" summary="Error rates for ellint_rc">
<colgroup>
<col>
<col>
<col>
<col>
</colgroup>
<thead><tr>
<th>
              </th>
<th>
                <p>
                  GNU C++ version 7.1.0<br> linux<br> double
                </p>
              </th>
<th>
                <p>
                  GNU C++ version 7.1.0<br> linux<br> long double
                </p>
              </th>
<th>
                <p>
                  Microsoft Visual C++ version 14.1<br> Win32<br> double
                </p>
              </th>
</tr></thead>
<tbody><tr>
<td>
                <p>
                  RC: Random data
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
                  2.1:</em></span> Max = 2.4&#949; (Mean = 0.624&#949;))
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 0.995&#949; (Mean = 0.433&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 0.962&#949; (Mean = 0.407&#949;)</span>
                </p>
              </td>
</tr></tbody>
</table></div>
</div>
<br class="table-break"><div class="table">
<a name="math_toolkit.logs_and_tables.all_table.table_ellint_rd"></a><p class="title"><b>Table&#160;23.36.&#160;Error rates for ellint_rd</b></p>
<div class="table-contents"><table class="table" summary="Error rates for ellint_rd">
<colgroup>
<col>
<col>
<col>
<col>
</colgroup>
<thead><tr>
<th>
              </th>
<th>
                <p>
                  GNU C++ version 7.1.0<br> linux<br> double
                </p>
              </th>
<th>
                <p>
                  GNU C++ version 7.1.0<br> linux<br> long double
                </p>
              </th>
<th>
                <p>
                  Microsoft Visual C++ version 14.1<br> Win32<br> double
                </p>
              </th>
</tr></thead>
<tbody>
<tr>
<td>
                <p>
                  RD: Random data
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
                  2.1:</em></span> Max = 2.59&#949; (Mean = 0.878&#949;))
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 2.73&#949; (Mean = 0.831&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 2.16&#949; (Mean = 0.803&#949;)</span>
                </p>
              </td>
</tr>
<tr>
<td>
                <p>
                  RD: y = z
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 0.896&#949; (Mean = 0.022&#949;)</span><br> <br>
                  (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 2.88&#949; (Mean = 0.839&#949;))
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 2.65&#949; (Mean = 0.82&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 16.5&#949; (Mean = 0.843&#949;)</span>
                </p>
              </td>
</tr>
<tr>
<td>
                <p>
                  RD: x = y
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 0.824&#949; (Mean = 0.0272&#949;)</span><br>
                  <br> (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 3.74&#949; (Mean = 0.84&#949;))
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 2.85&#949; (Mean = 0.865&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 3.51&#949; (Mean = 0.816&#949;)</span>
                </p>
              </td>
</tr>
<tr>
<td>
                <p>
                  RD: x = 0, y = z
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
                  2.1:</em></span> Max = 2&#949; (Mean = 0.656&#949;))
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 1.19&#949; (Mean = 0.522&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 1.16&#949; (Mean = 0.497&#949;)</span>
                </p>
              </td>
</tr>
<tr>
<td>
                <p>
                  RD: x = y = z
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
                  2.1:</em></span> Max = 1.03&#949; (Mean = 0.418&#949;))
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 0.998&#949; (Mean = 0.387&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 1.03&#949; (Mean = 0.418&#949;)</span>
                </p>
              </td>
</tr>
<tr>
<td>
                <p>
                  RD: x = 0
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
                  2.1:</em></span> Max = 2.85&#949; (Mean = 0.781&#949;))
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 2.79&#949; (Mean = 0.883&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 2.64&#949; (Mean = 0.894&#949;)</span>
                </p>
              </td>
</tr>
</tbody>
</table></div>
</div>
<br class="table-break"><div class="table">
<a name="math_toolkit.logs_and_tables.all_table.table_ellint_rf"></a><p class="title"><b>Table&#160;23.37.&#160;Error rates for ellint_rf</b></p>
<div class="table-contents"><table class="table" summary="Error rates for ellint_rf">
<colgroup>
<col>
<col>
<col>
<col>
</colgroup>
<thead><tr>
<th>
              </th>
<th>
                <p>
                  GNU C++ version 7.1.0<br> linux<br> double
                </p>
              </th>
<th>
                <p>
                  GNU C++ version 7.1.0<br> linux<br> long double
                </p>
              </th>
<th>
                <p>
                  Microsoft Visual C++ version 14.1<br> Win32<br> double
                </p>
              </th>
</tr></thead>
<tbody>
<tr>
<td>
                <p>
                  RF: Random data
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
                  2.1:</em></span> Max = 2.73&#949; (Mean = 0.804&#949;))
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 2.54&#949; (Mean = 0.674&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 2.02&#949; (Mean = 0.677&#949;)</span>
                </p>
              </td>
</tr>
<tr>
<td>
                <p>
                  RF: x = y = z
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
                  2.1:</em></span> Max = 0.999&#949; (Mean = 0.34&#949;))
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 0.991&#949; (Mean = 0.345&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 0.999&#949; (Mean = 0.34&#949;)</span>
                </p>
              </td>
</tr>
<tr>
<td>
                <p>
                  RF: x = y or y = z or x = z
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 0.536&#949; (Mean = 0.00658&#949;)</span><br>
                  <br> (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 2.89&#949; (Mean = 0.749&#949;))
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 1.95&#949; (Mean = 0.418&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 1.21&#949; (Mean = 0.394&#949;)</span>
                </p>
              </td>
</tr>
<tr>
<td>
                <p>
                  RF: x = 0, y = z
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
                  2.1:</em></span> Max = 1.29&#949; (Mean = 0.527&#949;))
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 0.894&#949; (Mean = 0.338&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 0.999&#949; (Mean = 0.407&#949;)</span>
                </p>
              </td>
</tr>
<tr>
<td>
                <p>
                  RF: z = 0
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
                  2.1:</em></span> Max = 2.54&#949; (Mean = 0.781&#949;))
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 1.7&#949; (Mean = 0.539&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 1.89&#949; (Mean = 0.587&#949;)</span>
                </p>
              </td>
</tr>
</tbody>
</table></div>
</div>
<br class="table-break"><div class="table">
<a name="math_toolkit.logs_and_tables.all_table.table_ellint_rg"></a><p class="title"><b>Table&#160;23.38.&#160;Error rates for ellint_rg</b></p>
<div class="table-contents"><table class="table" summary="Error rates for ellint_rg">
<colgroup>
<col>
<col>
<col>
<col>
</colgroup>
<thead><tr>
<th>
              </th>
<th>
                <p>
                  GNU C++ version 7.1.0<br> linux<br> double
                </p>
              </th>
<th>
                <p>
                  GNU C++ version 7.1.0<br> linux<br> long double
                </p>
              </th>
<th>
                <p>
                  Microsoft Visual C++ version 14.1<br> Win32<br> double
                </p>
              </th>
</tr></thead>
<tbody>
<tr>
<td>
                <p>
                  RG: Random Data
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 0.983&#949; (Mean = 0.0172&#949;)</span><br>
                  <br> (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 0.983&#949; (Mean = 0.0172&#949;))
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 3.95&#949; (Mean = 0.951&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 3.65&#949; (Mean = 0.929&#949;)</span>
                </p>
              </td>
</tr>
<tr>
<td>
                <p>
                  RG: two values 0
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
                  2.1:</em></span> Max = 0&#949; (Mean = 0&#949;))
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span>
                </p>
              </td>
</tr>
<tr>
<td>
                <p>
                  RG: All values the same or zero
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
                  2.1:</em></span> Max = 0&#949; (Mean = 0&#949;))
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 0.992&#949; (Mean = 0.288&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 1.06&#949; (Mean = 0.348&#949;)</span>
                </p>
              </td>
</tr>
<tr>
<td>
                <p>
                  RG: two values the same
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 0.594&#949; (Mean = 0.0103&#949;)</span><br>
                  <br> (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 0.594&#949; (Mean = 0.0103&#949;))
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 1.51&#949; (Mean = 0.404&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 1.96&#949; (Mean = 0.374&#949;)</span>
                </p>
              </td>
</tr>
<tr>
<td>
                <p>
                  RG: one value zero
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
                  2.1:</em></span> Max = 0&#949; (Mean = 0&#949;))
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 2.14&#949; (Mean = 0.722&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 1.96&#949; (Mean = 0.674&#949;)</span>
                </p>
              </td>
</tr>
</tbody>
</table></div>
</div>
<br class="table-break"><div class="table">
<a name="math_toolkit.logs_and_tables.all_table.table_ellint_rj"></a><p class="title"><b>Table&#160;23.39.&#160;Error rates for ellint_rj</b></p>
<div class="table-contents"><table class="table" summary="Error rates for ellint_rj">
<colgroup>
<col>
<col>
<col>
<col>
</colgroup>
<thead><tr>
<th>
              </th>
<th>
                <p>
                  GNU C++ version 7.1.0<br> linux<br> double
                </p>
              </th>
<th>
                <p>
                  GNU C++ version 7.1.0<br> linux<br> long double
                </p>
              </th>
<th>
                <p>
                  Microsoft Visual C++ version 14.1<br> Win32<br> double
                </p>
              </th>
</tr></thead>
<tbody>
<tr>
<td>
                <p>
                  RJ: Random data
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 0.52&#949; (Mean = 0.0184&#949;)</span><br> <br>
                  (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 3.57&#949; (Mean = 0.704&#949;) <a class="link" href="logs.html#errors_GNU_C_version_7_1_0_linux_double_ellint_rj_GSL_2_1_RJ_Random_data">And
                  other failures.</a>)
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 186&#949; (Mean = 6.67&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 215&#949; (Mean = 7.66&#949;)</span>
                </p>
              </td>
</tr>
<tr>
<td>
                <p>
                  RJ: 4 Equal Values
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
                  2.1:</em></span> Max = 1.03&#949; (Mean = 0.418&#949;))
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 0.998&#949; (Mean = 0.387&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 1.03&#949; (Mean = 0.418&#949;)</span>
                </p>
              </td>
</tr>
<tr>
<td>
                <p>
                  RJ: 3 Equal Values
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
                  2.1:</em></span> Max = 3.96&#949; (Mean = 1.06&#949;))
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 20.8&#949; (Mean = 0.986&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 39.9&#949; (Mean = 1.17&#949;)</span>
                </p>
              </td>
</tr>
<tr>
<td>
                <p>
                  RJ: 2 Equal Values
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 0.6&#949; (Mean = 0.0228&#949;)</span><br> <br>
                  (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 2.57&#949; (Mean = 0.754&#949;))
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 220&#949; (Mean = 6.64&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 214&#949; (Mean = 5.28&#949;)</span>
                </p>
              </td>
</tr>
<tr>
<td>
                <p>
                  RJ: Equal z and p
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 0.742&#949; (Mean = 0.0166&#949;)</span><br>
                  <br> (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 2.62&#949; (Mean = 0.699&#949;))
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 17.2&#949; (Mean = 1.16&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 16.1&#949; (Mean = 1.14&#949;)</span>
                </p>
              </td>
</tr>
</tbody>
</table></div>
</div>
<br class="table-break"><div class="table">
<a name="math_toolkit.logs_and_tables.all_table.table_erf"></a><p class="title"><b>Table&#160;23.40.&#160;Error rates for erf</b></p>
<div class="table-contents"><table class="table" summary="Error rates for erf">
<colgroup>
<col>
<col>
<col>
<col>
<col>
</colgroup>
<thead><tr>
<th>
              </th>
<th>
                <p>
                  GNU C++ version 7.1.0<br> linux<br> long double
                </p>
              </th>
<th>
                <p>
                  GNU C++ version 7.1.0<br> linux<br> double
                </p>
              </th>
<th>
                <p>
                  Sun compiler version 0x5150<br> Sun Solaris<br> long double
                </p>
              </th>
<th>
                <p>
                  Microsoft Visual C++ version 14.1<br> Win32<br> double
                </p>
              </th>
</tr></thead>
<tbody>
<tr>
<td>
                <p>
                  Erf Function: Small Values
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 0.925&#949; (Mean = 0.193&#949;)</span><br> <br>
                  (<span class="emphasis"><em>&lt;cmath&gt;:</em></span> Max = 0.944&#949; (Mean = 0.191&#949;))<br>
                  (<span class="emphasis"><em>&lt;math.h&gt;:</em></span> Max = 0.944&#949; (Mean = 0.191&#949;))
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 0.841&#949; (Mean = 0.0687&#949;)</span><br>
                  <br> (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 2.06&#949; (Mean = 0.319&#949;))
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 0.925&#949; (Mean = 0.193&#949;)</span><br> <br>
                  (<span class="emphasis"><em>&lt;math.h&gt;:</em></span> Max = 0.944&#949; (Mean = 0.194&#949;))
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 0.996&#949; (Mean = 0.182&#949;)</span><br> <br>
                  (<span class="emphasis"><em>&lt;math.h&gt;:</em></span> Max = 1.57&#949; (Mean = 0.317&#949;))
                </p>
              </td>
</tr>
<tr>
<td>
                <p>
                  Erf Function: Medium Values
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 1.5&#949; (Mean = 0.193&#949;)</span><br> <br>
                  (<span class="emphasis"><em>&lt;cmath&gt;:</em></span> Max = 0.921&#949; (Mean = 0.0723&#949;))<br>
                  (<span class="emphasis"><em>&lt;math.h&gt;:</em></span> Max = 0.921&#949; (Mean = 0.0723&#949;))
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 1&#949; (Mean = 0.119&#949;)</span><br> <br>
                  (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 2.31&#949; (Mean = 0.368&#949;))
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 1.5&#949; (Mean = 0.197&#949;)</span><br> <br>
                  (<span class="emphasis"><em>&lt;math.h&gt;:</em></span> Max = 0.921&#949; (Mean = 0.071&#949;))
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 1&#949; (Mean = 0.171&#949;)</span><br> <br>
                  (<span class="emphasis"><em>&lt;math.h&gt;:</em></span> Max = 1.19&#949; (Mean = 0.244&#949;))
                </p>
              </td>
</tr>
<tr>
<td>
                <p>
                  Erf Function: Large Values
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>&lt;cmath&gt;:</em></span>
                  Max = 0&#949; (Mean = 0&#949;))<br> (<span class="emphasis"><em>&lt;math.h&gt;:</em></span>
                  Max = 0&#949; (Mean = 0&#949;))
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
                  2.1:</em></span> Max = 0&#949; (Mean = 0&#949;))
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>&lt;math.h&gt;:</em></span>
                  Max = 0&#949; (Mean = 0&#949;))
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>&lt;math.h&gt;:</em></span>
                  Max = 0&#949; (Mean = 0&#949;))
                </p>
              </td>
</tr>
</tbody>
</table></div>
</div>
<br class="table-break"><div class="table">
<a name="math_toolkit.logs_and_tables.all_table.table_erf_inv"></a><p class="title"><b>Table&#160;23.41.&#160;Error rates for erf_inv</b></p>
<div class="table-contents"><table class="table" summary="Error rates for erf_inv">
<colgroup>
<col>
<col>
<col>
<col>
<col>
</colgroup>
<thead><tr>
<th>
              </th>
<th>
                <p>
                  GNU C++ version 7.1.0<br> linux<br> double
                </p>
              </th>
<th>
                <p>
                  GNU C++ version 7.1.0<br> linux<br> long double
                </p>
              </th>
<th>
                <p>
                  Sun compiler version 0x5150<br> Sun Solaris<br> long double
                </p>
              </th>
<th>
                <p>
                  Microsoft Visual C++ version 14.1<br> Win32<br> double
                </p>
              </th>
</tr></thead>
<tbody><tr>
<td>
                <p>
                  Inverse Erf Function
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 0.996&#949; (Mean = 0.389&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 1.08&#949; (Mean = 0.395&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 1.09&#949; (Mean = 0.502&#949;)</span>
                </p>
              </td>
</tr></tbody>
</table></div>
</div>
<br class="table-break"><div class="table">
<a name="math_toolkit.logs_and_tables.all_table.table_erfc"></a><p class="title"><b>Table&#160;23.42.&#160;Error rates for erfc</b></p>
<div class="table-contents"><table class="table" summary="Error rates for erfc">
<colgroup>
<col>
<col>
<col>
<col>
<col>
</colgroup>
<thead><tr>
<th>
              </th>
<th>
                <p>
                  GNU C++ version 7.1.0<br> linux<br> long double
                </p>
              </th>
<th>
                <p>
                  GNU C++ version 7.1.0<br> linux<br> double
                </p>
              </th>
<th>
                <p>
                  Sun compiler version 0x5150<br> Sun Solaris<br> long double
                </p>
              </th>
<th>
                <p>
                  Microsoft Visual C++ version 14.1<br> Win32<br> double
                </p>
              </th>
</tr></thead>
<tbody>
<tr>
<td>
                <p>
                  Erf Function: Small Values
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>&lt;cmath&gt;:</em></span>
                  Max = 0&#949; (Mean = 0&#949;))<br> (<span class="emphasis"><em>&lt;math.h&gt;:</em></span>
                  Max = 0&#949; (Mean = 0&#949;))
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 0.658&#949; (Mean = 0.0537&#949;)</span><br>
                  <br> (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 1.01&#949; (Mean = 0.485&#949;))
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>&lt;math.h&gt;:</em></span>
                  Max = 0&#949; (Mean = 0&#949;))
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>&lt;math.h&gt;:</em></span>
                  Max = 0&#949; (Mean = 0&#949;))
                </p>
              </td>
</tr>
<tr>
<td>
                <p>
                  Erf Function: Medium Values
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 1.76&#949; (Mean = 0.365&#949;)</span><br> <br>
                  (<span class="emphasis"><em>&lt;cmath&gt;:</em></span> Max = 1.35&#949; (Mean = 0.307&#949;))<br>
                  (<span class="emphasis"><em>&lt;math.h&gt;:</em></span> Max = 1.35&#949; (Mean = 0.307&#949;))
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 0.983&#949; (Mean = 0.213&#949;)</span><br> <br>
                  (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 2.64&#949; (Mean = 0.662&#949;))
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 1.76&#949; (Mean = 0.38&#949;)</span><br> <br>
                  (<span class="emphasis"><em>&lt;math.h&gt;:</em></span> Max = 2.81&#949; (Mean = 0.739&#949;))
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 1.65&#949; (Mean = 0.373&#949;)</span><br> <br>
                  (<span class="emphasis"><em>&lt;math.h&gt;:</em></span> Max = 2.36&#949; (Mean = 0.539&#949;))
                </p>
              </td>
</tr>
<tr>
<td>
                <p>
                  Erf Function: Large Values
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 1.57&#949; (Mean = 0.542&#949;)</span><br> <br>
                  (<span class="emphasis"><em>&lt;cmath&gt;:</em></span> Max = 1.26&#949; (Mean = 0.441&#949;))<br>
                  (<span class="emphasis"><em>&lt;math.h&gt;:</em></span> Max = 1.26&#949; (Mean = 0.441&#949;))
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 0.868&#949; (Mean = 0.147&#949;)</span><br> <br>
                  (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 3.9&#949; (Mean = 0.472&#949;))
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 1.57&#949; (Mean = 0.564&#949;)</span><br> <br>
                  (<span class="emphasis"><em>&lt;math.h&gt;:</em></span> Max = 4.91&#949; (Mean = 1.54&#949;))
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 1.14&#949; (Mean = 0.248&#949;)</span><br> <br>
                  (<span class="emphasis"><em>&lt;math.h&gt;:</em></span> Max = 1.84&#949; (Mean = 0.331&#949;))
                </p>
              </td>
</tr>
</tbody>
</table></div>
</div>
<br class="table-break"><div class="table">
<a name="math_toolkit.logs_and_tables.all_table.table_erfc_inv"></a><p class="title"><b>Table&#160;23.43.&#160;Error rates for erfc_inv</b></p>
<div class="table-contents"><table class="table" summary="Error rates for erfc_inv">
<colgroup>
<col>
<col>
<col>
<col>
<col>
</colgroup>
<thead><tr>
<th>
              </th>
<th>
                <p>
                  GNU C++ version 7.1.0<br> linux<br> double
                </p>
              </th>
<th>
                <p>
                  GNU C++ version 7.1.0<br> linux<br> long double
                </p>
              </th>
<th>
                <p>
                  Sun compiler version 0x5150<br> Sun Solaris<br> long double
                </p>
              </th>
<th>
                <p>
                  Microsoft Visual C++ version 14.1<br> Win32<br> double
                </p>
              </th>
</tr></thead>
<tbody>
<tr>
<td>
                <p>
                  Inverse Erfc Function
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 0.996&#949; (Mean = 0.397&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 1.08&#949; (Mean = 0.403&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 1&#949; (Mean = 0.491&#949;)</span>
                </p>
              </td>
</tr>
<tr>
<td>
                <p>
                  Inverse Erfc Function: extreme values
                </p>
              </td>
<td>
              </td>
<td>
                <p>
                  <span class="blue">Max = 1.62&#949; (Mean = 0.383&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 1.62&#949; (Mean = 0.383&#949;)</span>
                </p>
              </td>
<td>
              </td>
</tr>
</tbody>
</table></div>
</div>
<br class="table-break"><div class="table">
<a name="math_toolkit.logs_and_tables.all_table.table_expint_Ei_"></a><p class="title"><b>Table&#160;23.44.&#160;Error rates for expint (Ei)</b></p>
<div class="table-contents"><table class="table" summary="Error rates for expint (Ei)">
<colgroup>
<col>
<col>
<col>
<col>
<col>
</colgroup>
<thead><tr>
<th>
              </th>
<th>
                <p>
                  GNU C++ version 7.1.0<br> linux<br> long double
                </p>
              </th>
<th>
                <p>
                  GNU C++ version 7.1.0<br> linux<br> double
                </p>
              </th>
<th>
                <p>
                  Sun compiler version 0x5150<br> Sun Solaris<br> long double
                </p>
              </th>
<th>
                <p>
                  Microsoft Visual C++ version 14.1<br> Win32<br> double
                </p>
              </th>
</tr></thead>
<tbody>
<tr>
<td>
                <p>
                  Exponential Integral Ei
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 5.05&#949; (Mean = 0.821&#949;)</span><br> <br>
                  (<span class="emphasis"><em>&lt;cmath&gt;:</em></span> Max = 14.1&#949; (Mean = 2.43&#949;) <a class="link" href="logs.html#errors_GNU_C_version_7_1_0_linux_long_double_expint_Ei___cmath__Exponential_Integral_Ei">And
                  other failures.</a>)
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 0.994&#949; (Mean = 0.142&#949;)</span><br> <br>
                  (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 8.96&#949; (Mean = 0.703&#949;))
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 5.05&#949; (Mean = 0.835&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 1.43&#949; (Mean = 0.54&#949;)</span>
                </p>
              </td>
</tr>
<tr>
<td>
                <p>
                  Exponential Integral Ei: double exponent range
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 1.72&#949; (Mean = 0.593&#949;)</span><br> <br>
                  (<span class="emphasis"><em>&lt;cmath&gt;:</em></span> Max = 3.11&#949; (Mean = 1.13&#949;))
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 0.998&#949; (Mean = 0.156&#949;)</span><br> <br>
                  (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 1.5&#949; (Mean = 0.612&#949;))
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 1.72&#949; (Mean = 0.607&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 1.7&#949; (Mean = 0.66&#949;)</span>
                </p>
              </td>
</tr>
<tr>
<td>
                <p>
                  Exponential Integral Ei: long exponent range
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 1.98&#949; (Mean = 0.595&#949;)</span><br> <br>
                  (<span class="emphasis"><em>&lt;cmath&gt;:</em></span> Max = 1.93&#949; (Mean = 0.855&#949;))
                </p>
              </td>
<td>
              </td>
<td>
                <p>
                  <span class="blue">Max = 1.98&#949; (Mean = 0.575&#949;)</span>
                </p>
              </td>
<td>
              </td>
</tr>
</tbody>
</table></div>
</div>
<br class="table-break"><div class="table">
<a name="math_toolkit.logs_and_tables.all_table.table_expint_En_"></a><p class="title"><b>Table&#160;23.45.&#160;Error rates for expint (En)</b></p>
<div class="table-contents"><table class="table" summary="Error rates for expint (En)">
<colgroup>
<col>
<col>
<col>
<col>
<col>
</colgroup>
<thead><tr>
<th>
              </th>
<th>
                <p>
                  GNU C++ version 7.1.0<br> linux<br> double
                </p>
              </th>
<th>
                <p>
                  GNU C++ version 7.1.0<br> linux<br> long double
                </p>
              </th>
<th>
                <p>
                  Sun compiler version 0x5150<br> Sun Solaris<br> long double
                </p>
              </th>
<th>
                <p>
                  Microsoft Visual C++ version 14.1<br> Win32<br> double
                </p>
              </th>
</tr></thead>
<tbody>
<tr>
<td>
                <p>
                  Exponential Integral En
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 0.589&#949; (Mean = 0.0331&#949;)</span><br>
                  <br> (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 58.5&#949; (Mean = 17.1&#949;))
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 9.97&#949; (Mean = 2.13&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 9.97&#949; (Mean = 2.13&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 7.16&#949; (Mean = 1.85&#949;)</span>
                </p>
              </td>
</tr>
<tr>
<td>
                <p>
                  Exponential Integral En: small z values
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
                  2.1:</em></span> Max = 115&#949; (Mean = 23.6&#949;))
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 1.99&#949; (Mean = 0.559&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 1.99&#949; (Mean = 0.559&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 2.62&#949; (Mean = 0.531&#949;)</span>
                </p>
              </td>
</tr>
<tr>
<td>
                <p>
                  Exponential Integral E1
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 0.556&#949; (Mean = 0.0625&#949;)</span><br>
                  <br> (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 0.988&#949; (Mean = 0.469&#949;))
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 0.965&#949; (Mean = 0.414&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 0.965&#949; (Mean = 0.408&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 0.988&#949; (Mean = 0.486&#949;)</span>
                </p>
              </td>
</tr>
</tbody>
</table></div>
</div>
<br class="table-break"><div class="table">
<a name="math_toolkit.logs_and_tables.all_table.table_expm1"></a><p class="title"><b>Table&#160;23.46.&#160;Error rates for expm1</b></p>
<div class="table-contents"><table class="table" summary="Error rates for expm1">
<colgroup>
<col>
<col>
<col>
<col>
<col>
</colgroup>
<thead><tr>
<th>
              </th>
<th>
                <p>
                  GNU C++ version 7.1.0<br> linux<br> long double
                </p>
              </th>
<th>
                <p>
                  GNU C++ version 7.1.0<br> linux<br> double
                </p>
              </th>
<th>
                <p>
                  Sun compiler version 0x5150<br> Sun Solaris<br> long double
                </p>
              </th>
<th>
                <p>
                  Microsoft Visual C++ version 14.1<br> Win32<br> double
                </p>
              </th>
</tr></thead>
<tbody><tr>
<td>
                <p>
                  Random test data
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 0.992&#949; (Mean = 0.402&#949;)</span><br> <br>
                  (<span class="emphasis"><em>&lt;cmath&gt;:</em></span> Max = 0.992&#949; (Mean = 0.402&#949;))<br>
                  (<span class="emphasis"><em>&lt;math.h&gt;:</em></span> Max = 0.992&#949; (Mean = 0.402&#949;))
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 0.793&#949; (Mean = 0.126&#949;)</span><br> <br>
                  (<span class="emphasis"><em>Rmath 3.2.3:</em></span> Max = 0.793&#949; (Mean = 0.126&#949;))
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 1.31&#949; (Mean = 0.428&#949;)</span><br> <br>
                  (<span class="emphasis"><em>&lt;math.h&gt;:</em></span> Max = 0.996&#949; (Mean = 0.426&#949;))
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 1.31&#949; (Mean = 0.496&#949;)</span><br> <br>
                  (<span class="emphasis"><em>&lt;math.h&gt;:</em></span> Max = 1.31&#949; (Mean = 0.496&#949;))
                </p>
              </td>
</tr></tbody>
</table></div>
</div>
<br class="table-break"><div class="table">
<a name="math_toolkit.logs_and_tables.all_table.table_gamma_p"></a><p class="title"><b>Table&#160;23.47.&#160;Error rates for gamma_p</b></p>
<div class="table-contents"><table class="table" summary="Error rates for gamma_p">
<colgroup>
<col>
<col>
<col>
<col>
<col>
</colgroup>
<thead><tr>
<th>
              </th>
<th>
                <p>
                  GNU C++ version 7.1.0<br> linux<br> double
                </p>
              </th>
<th>
                <p>
                  GNU C++ version 7.1.0<br> linux<br> long double
                </p>
              </th>
<th>
                <p>
                  Sun compiler version 0x5150<br> Sun Solaris<br> long double
                </p>
              </th>
<th>
                <p>
                  Microsoft Visual C++ version 14.1<br> Win32<br> double
                </p>
              </th>
</tr></thead>
<tbody>
<tr>
<td>
                <p>
                  tgamma(a, z) medium values
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 0.955&#949; (Mean = 0.05&#949;)</span><br> <br>
                  (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 342&#949; (Mean = 45.8&#949;))<br> (<span class="emphasis"><em>Rmath
                  3.2.3:</em></span> Max = 389&#949; (Mean = 44&#949;))
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 41.6&#949; (Mean = 8.09&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 239&#949; (Mean = 30.2&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 35.1&#949; (Mean = 6.98&#949;)</span>
                </p>
              </td>
</tr>
<tr>
<td>
                <p>
                  tgamma(a, z) small values
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
                  2.1:</em></span> Max = 4.82&#949; (Mean = 0.758&#949;))<br> (<span class="emphasis"><em>Rmath
                  3.2.3:</em></span> Max = 1.01&#949; (Mean = 0.306&#949;))
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 2&#949; (Mean = 0.464&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 2&#949; (Mean = 0.461&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 1.54&#949; (Mean = 0.439&#949;)</span>
                </p>
              </td>
</tr>
<tr>
<td>
                <p>
                  tgamma(a, z) large values
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
                  2.1:</em></span> Max = 1.02e+03&#949; (Mean = 105&#949;))<br> (<span class="emphasis"><em>Rmath
                  3.2.3:</em></span> Max = 1.11e+03&#949; (Mean = 67.5&#949;))
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 3.08e+04&#949; (Mean = 1.86e+03&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 3.02e+04&#949; (Mean = 1.91e+03&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 243&#949; (Mean = 20.2&#949;)</span>
                </p>
              </td>
</tr>
<tr>
<td>
                <p>
                  tgamma(a, z) integer and half integer values
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
                  2.1:</em></span> Max = 128&#949; (Mean = 22.6&#949;))<br> (<span class="emphasis"><em>Rmath
                  3.2.3:</em></span> Max = 66.2&#949; (Mean = 12.2&#949;))
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 11.8&#949; (Mean = 2.66&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 71.6&#949; (Mean = 9.47&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 13&#949; (Mean = 2.97&#949;)</span>
                </p>
              </td>
</tr>
</tbody>
</table></div>
</div>
<br class="table-break"><div class="table">
<a name="math_toolkit.logs_and_tables.all_table.table_gamma_p_inv"></a><p class="title"><b>Table&#160;23.48.&#160;Error rates for gamma_p_inv</b></p>
<div class="table-contents"><table class="table" summary="Error rates for gamma_p_inv">
<colgroup>
<col>
<col>
<col>
<col>
<col>
</colgroup>
<thead><tr>
<th>
              </th>
<th>
                <p>
                  GNU C++ version 7.1.0<br> linux<br> double
                </p>
              </th>
<th>
                <p>
                  GNU C++ version 7.1.0<br> linux<br> long double
                </p>
              </th>
<th>
                <p>
                  Sun compiler version 0x5150<br> Sun Solaris<br> long double
                </p>
              </th>
<th>
                <p>
                  Microsoft Visual C++ version 14.1<br> Win32<br> double
                </p>
              </th>
</tr></thead>
<tbody>
<tr>
<td>
                <p>
                  incomplete gamma inverse(a, z) medium values
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 0.993&#949; (Mean = 0.15&#949;)</span><br> <br>
                  (<span class="emphasis"><em>Rmath 3.2.3:</em></span> Max = 4.88&#949; (Mean = 0.868&#949;))
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 1.8&#949; (Mean = 0.406&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 1.89&#949; (Mean = 0.466&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 1.71&#949; (Mean = 0.34&#949;)</span>
                </p>
              </td>
</tr>
<tr>
<td>
                <p>
                  incomplete gamma inverse(a, z) large values
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>Rmath
                  3.2.3:</em></span> Max = 0.816&#949; (Mean = 0.0874&#949;))
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 0.509&#949; (Mean = 0.0447&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 0.509&#949; (Mean = 0.0447&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 0.924&#949; (Mean = 0.108&#949;)</span>
                </p>
              </td>
</tr>
<tr>
<td>
                <p>
                  incomplete gamma inverse(a, z) small values
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 441&#949; (Mean = 53.9&#949;)</span><br> <br>
                  (<span class="emphasis"><em>Rmath 3.2.3:</em></span> Max = 547&#949; (Mean = 61.6&#949;))
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 9.17e+03&#949; (Mean = 1.45e+03&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 1.09e+04&#949; (Mean = 1.3e+03&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 1.1e+03&#949; (Mean = 131&#949;)</span>
                </p>
              </td>
</tr>
</tbody>
</table></div>
</div>
<br class="table-break"><div class="table">
<a name="math_toolkit.logs_and_tables.all_table.table_gamma_p_inva"></a><p class="title"><b>Table&#160;23.49.&#160;Error rates for gamma_p_inva</b></p>
<div class="table-contents"><table class="table" summary="Error rates for gamma_p_inva">
<colgroup>
<col>
<col>
<col>
<col>
<col>
</colgroup>
<thead><tr>
<th>
              </th>
<th>
                <p>
                  GNU C++ version 7.1.0<br> linux<br> double
                </p>
              </th>
<th>
                <p>
                  GNU C++ version 7.1.0<br> linux<br> long double
                </p>
              </th>
<th>
                <p>
                  Sun compiler version 0x5150<br> Sun Solaris<br> long double
                </p>
              </th>
<th>
                <p>
                  Microsoft Visual C++ version 14.1<br> Win32<br> double
                </p>
              </th>
</tr></thead>
<tbody><tr>
<td>
                <p>
                  Incomplete gamma inverses.
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 7.87&#949; (Mean = 1.15&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 4.08&#949; (Mean = 1.12&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 4.92&#949; (Mean = 1.03&#949;)</span>
                </p>
              </td>
</tr></tbody>
</table></div>
</div>
<br class="table-break"><div class="table">
<a name="math_toolkit.logs_and_tables.all_table.table_gamma_q"></a><p class="title"><b>Table&#160;23.50.&#160;Error rates for gamma_q</b></p>
<div class="table-contents"><table class="table" summary="Error rates for gamma_q">
<colgroup>
<col>
<col>
<col>
<col>
<col>
</colgroup>
<thead><tr>
<th>
              </th>
<th>
                <p>
                  GNU C++ version 7.1.0<br> linux<br> double
                </p>
              </th>
<th>
                <p>
                  GNU C++ version 7.1.0<br> linux<br> long double
                </p>
              </th>
<th>
                <p>
                  Sun compiler version 0x5150<br> Sun Solaris<br> long double
                </p>
              </th>
<th>
                <p>
                  Microsoft Visual C++ version 14.1<br> Win32<br> double
                </p>
              </th>
</tr></thead>
<tbody>
<tr>
<td>
                <p>
                  tgamma(a, z) medium values
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 0.927&#949; (Mean = 0.035&#949;)</span><br> <br>
                  (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 201&#949; (Mean = 13.5&#949;))<br> (<span class="emphasis"><em>Rmath
                  3.2.3:</em></span> Max = 131&#949; (Mean = 12.7&#949;))
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 32.3&#949; (Mean = 6.61&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 199&#949; (Mean = 26.6&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 23.7&#949; (Mean = 4&#949;)</span>
                </p>
              </td>
</tr>
<tr>
<td>
                <p>
                  tgamma(a, z) small values
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
                  2.1:</em></span> <span class="red">Max = 1.38e+10&#949; (Mean = 1.05e+09&#949;))</span><br>
                  (<span class="emphasis"><em>Rmath 3.2.3:</em></span> Max = 65.6&#949; (Mean = 11&#949;))
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 2.45&#949; (Mean = 0.885&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 2.45&#949; (Mean = 0.819&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 2.26&#949; (Mean = 0.74&#949;)</span>
                </p>
              </td>
</tr>
<tr>
<td>
                <p>
                  tgamma(a, z) large values
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
                  2.1:</em></span> Max = 2.71e+04&#949; (Mean = 2.16e+03&#949;))<br> (<span class="emphasis"><em>Rmath
                  3.2.3:</em></span> Max = 1.02e+03&#949; (Mean = 62.7&#949;))
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 6.82e+03&#949; (Mean = 414&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 1.15e+04&#949; (Mean = 733&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 469&#949; (Mean = 31.5&#949;)</span>
                </p>
              </td>
</tr>
<tr>
<td>
                <p>
                  tgamma(a, z) integer and half integer values
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
                  2.1:</em></span> Max = 118&#949; (Mean = 12.5&#949;))<br> (<span class="emphasis"><em>Rmath
                  3.2.3:</em></span> Max = 138&#949; (Mean = 16.9&#949;))
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 11.1&#949; (Mean = 2.07&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 54.7&#949; (Mean = 6.16&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 8.72&#949; (Mean = 1.48&#949;)</span>
                </p>
              </td>
</tr>
</tbody>
</table></div>
</div>
<br class="table-break"><div class="table">
<a name="math_toolkit.logs_and_tables.all_table.table_gamma_q_inv"></a><p class="title"><b>Table&#160;23.51.&#160;Error rates for gamma_q_inv</b></p>
<div class="table-contents"><table class="table" summary="Error rates for gamma_q_inv">
<colgroup>
<col>
<col>
<col>
<col>
<col>
</colgroup>
<thead><tr>
<th>
              </th>
<th>
                <p>
                  GNU C++ version 7.1.0<br> linux<br> double
                </p>
              </th>
<th>
                <p>
                  GNU C++ version 7.1.0<br> linux<br> long double
                </p>
              </th>
<th>
                <p>
                  Sun compiler version 0x5150<br> Sun Solaris<br> long double
                </p>
              </th>
<th>
                <p>
                  Microsoft Visual C++ version 14.1<br> Win32<br> double
                </p>
              </th>
</tr></thead>
<tbody>
<tr>
<td>
                <p>
                  incomplete gamma inverse(a, z) medium values
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 0.912&#949; (Mean = 0.154&#949;)</span><br> <br>
                  (<span class="emphasis"><em>Rmath 3.2.3:</em></span> Max = 4.66&#949; (Mean = 0.792&#949;))
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 6.2&#949; (Mean = 0.627&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 6.2&#949; (Mean = 0.683&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 2.88&#949; (Mean = 0.469&#949;)</span>
                </p>
              </td>
</tr>
<tr>
<td>
                <p>
                  incomplete gamma inverse(a, z) large values
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 0.894&#949; (Mean = 0.0915&#949;)</span><br>
                  <br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span> Max = 0.894&#949; (Mean = 0.106&#949;))
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 0.814&#949; (Mean = 0.0856&#949;)</span>
                </p>
              </td>
</tr>
<tr>
<td>
                <p>
                  incomplete gamma inverse(a, z) small values
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 292&#949; (Mean = 36.4&#949;)</span><br> <br>
                  (<span class="emphasis"><em>Rmath 3.2.3:</em></span> Max = 415&#949; (Mean = 48.7&#949;))
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 8.28e+03&#949; (Mean = 1.09e+03&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 8.98e+03&#949; (Mean = 877&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 451&#949; (Mean = 64.7&#949;)</span>
                </p>
              </td>
</tr>
</tbody>
</table></div>
</div>
<br class="table-break"><div class="table">
<a name="math_toolkit.logs_and_tables.all_table.table_gamma_q_inva"></a><p class="title"><b>Table&#160;23.52.&#160;Error rates for gamma_q_inva</b></p>
<div class="table-contents"><table class="table" summary="Error rates for gamma_q_inva">
<colgroup>
<col>
<col>
<col>
<col>
<col>
</colgroup>
<thead><tr>
<th>
              </th>
<th>
                <p>
                  GNU C++ version 7.1.0<br> linux<br> double
                </p>
              </th>
<th>
                <p>
                  GNU C++ version 7.1.0<br> linux<br> long double
                </p>
              </th>
<th>
                <p>
                  Sun compiler version 0x5150<br> Sun Solaris<br> long double
                </p>
              </th>
<th>
                <p>
                  Microsoft Visual C++ version 14.1<br> Win32<br> double
                </p>
              </th>
</tr></thead>
<tbody><tr>
<td>
                <p>
                  Incomplete gamma inverses.
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 8.42&#949; (Mean = 1.3&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 7.86&#949; (Mean = 1.24&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 5.05&#949; (Mean = 1.08&#949;)</span>
                </p>
              </td>
</tr></tbody>
</table></div>
</div>
<br class="table-break"><div class="table">
<a name="math_toolkit.logs_and_tables.all_table.table_hermite"></a><p class="title"><b>Table&#160;23.53.&#160;Error rates for hermite</b></p>
<div class="table-contents"><table class="table" summary="Error rates for hermite">
<colgroup>
<col>
<col>
<col>
<col>
<col>
</colgroup>
<thead><tr>
<th>
              </th>
<th>
                <p>
                  GNU C++ version 7.1.0<br> linux<br> double
                </p>
              </th>
<th>
                <p>
                  GNU C++ version 7.1.0<br> linux<br> long double
                </p>
              </th>
<th>
                <p>
                  Sun compiler version 0x5150<br> Sun Solaris<br> long double
                </p>
              </th>
<th>
                <p>
                  Microsoft Visual C++ version 14.1<br> Win32<br> double
                </p>
              </th>
</tr></thead>
<tbody><tr>
<td>
                <p>
                  Hermite Polynomials
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 6.24&#949; (Mean = 2.07&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 6.24&#949; (Mean = 2.07&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 4.46&#949; (Mean = 1.41&#949;)</span>
                </p>
              </td>
</tr></tbody>
</table></div>
</div>
<br class="table-break"><div class="table">
<a name="math_toolkit.logs_and_tables.all_table.table_heuman_lambda"></a><p class="title"><b>Table&#160;23.54.&#160;Error rates for heuman_lambda</b></p>
<div class="table-contents"><table class="table" summary="Error rates for heuman_lambda">
<colgroup>
<col>
<col>
<col>
<col>
<col>
</colgroup>
<thead><tr>
<th>
              </th>
<th>
                <p>
                  GNU C++ version 7.1.0<br> linux<br> double
                </p>
              </th>
<th>
                <p>
                  GNU C++ version 7.1.0<br> linux<br> long double
                </p>
              </th>
<th>
                <p>
                  Sun compiler version 0x5150<br> Sun Solaris<br> long double
                </p>
              </th>
<th>
                <p>
                  Microsoft Visual C++ version 14.1<br> Win32<br> double
                </p>
              </th>
</tr></thead>
<tbody>
<tr>
<td>
                <p>
                  Elliptic Integral Jacobi Zeta: Mathworld Data
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 1.89&#949; (Mean = 0.887&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 1.89&#949; (Mean = 0.887&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 1.08&#949; (Mean = 0.734&#949;)</span>
                </p>
              </td>
</tr>
<tr>
<td>
                <p>
                  Elliptic Integral Heuman Lambda: Random Data
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 3.82&#949; (Mean = 0.609&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 3.82&#949; (Mean = 0.608&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 2.12&#949; (Mean = 0.588&#949;)</span>
                </p>
              </td>
</tr>
</tbody>
</table></div>
</div>
<br class="table-break"><div class="table">
<a name="math_toolkit.logs_and_tables.all_table.table_ibeta"></a><p class="title"><b>Table&#160;23.55.&#160;Error rates for ibeta</b></p>
<div class="table-contents"><table class="table" summary="Error rates for ibeta">
<colgroup>
<col>
<col>
<col>
<col>
<col>
</colgroup>
<thead><tr>
<th>
              </th>
<th>
                <p>
                  GNU C++ version 7.1.0<br> linux<br> double
                </p>
              </th>
<th>
                <p>
                  GNU C++ version 7.1.0<br> linux<br> long double
                </p>
              </th>
<th>
                <p>
                  Sun compiler version 0x5150<br> Sun Solaris<br> long double
                </p>
              </th>
<th>
                <p>
                  Microsoft Visual C++ version 14.1<br> Win32<br> double
                </p>
              </th>
</tr></thead>
<tbody>
<tr>
<td>
                <p>
                  Incomplete Beta Function: Small Values
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
                  2.1:</em></span> Max = 682&#949; (Mean = 32.6&#949;))<br> (<span class="emphasis"><em>Rmath
                  3.2.3:</em></span> Max = 22.9&#949; (Mean = 3.35&#949;))
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 8.97&#949; (Mean = 2.09&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 21.3&#949; (Mean = 2.75&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 8.4&#949; (Mean = 1.93&#949;)</span>
                </p>
              </td>
</tr>
<tr>
<td>
                <p>
                  Incomplete Beta Function: Medium Values
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
                  2.1:</em></span> Max = 690&#949; (Mean = 151&#949;))<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span>
                  Max = 232&#949; (Mean = 27.9&#949;))
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 50&#949; (Mean = 12.1&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 124&#949; (Mean = 18.4&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 106&#949; (Mean = 16.3&#949;)</span>
                </p>
              </td>
</tr>
<tr>
<td>
                <p>
                  Incomplete Beta Function: Large and Diverse Values
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 1.26&#949; (Mean = 0.063&#949;)</span><br> <br>
                  (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 3.9e+05&#949; (Mean = 1.82e+04&#949;)
                  <a class="link" href="logs.html#errors_GNU_C_version_7_1_0_linux_double_ibeta_GSL_2_1_Incomplete_Beta_Function_Large_and_Diverse_Values">And
                  other failures.</a>)<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span>
                  Max = 574&#949; (Mean = 49.4&#949;))
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 1.96e+04&#949; (Mean = 997&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 4.98e+04&#949; (Mean = 2.07e+03&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 1.32e+03&#949; (Mean = 68.5&#949;)</span>
                </p>
              </td>
</tr>
<tr>
<td>
                <p>
                  Incomplete Beta Function: Small Integer Values
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
                  2.1:</em></span> Max = 254&#949; (Mean = 50.9&#949;))<br> (<span class="emphasis"><em>Rmath
                  3.2.3:</em></span> Max = 62.2&#949; (Mean = 8.95&#949;))
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 4.45&#949; (Mean = 0.814&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 44.5&#949; (Mean = 10.1&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 3.85&#949; (Mean = 0.791&#949;)</span>
                </p>
              </td>
</tr>
</tbody>
</table></div>
</div>
<br class="table-break"><div class="table">
<a name="math_toolkit.logs_and_tables.all_table.table_ibeta_inv"></a><p class="title"><b>Table&#160;23.56.&#160;Error rates for ibeta_inv</b></p>
<div class="table-contents"><table class="table" summary="Error rates for ibeta_inv">
<colgroup>
<col>
<col>
<col>
<col>
<col>
</colgroup>
<thead><tr>
<th>
              </th>
<th>
                <p>
                  GNU C++ version 7.1.0<br> linux<br> double
                </p>
              </th>
<th>
                <p>
                  GNU C++ version 7.1.0<br> linux<br> long double
                </p>
              </th>
<th>
                <p>
                  Sun compiler version 0x5150<br> Sun Solaris<br> long double
                </p>
              </th>
<th>
                <p>
                  Microsoft Visual C++ version 14.1<br> Win32<br> double
                </p>
              </th>
</tr></thead>
<tbody><tr>
<td>
                <p>
                  Inverse incomplete beta
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 11&#949; (Mean = 0.345&#949;)</span><br> <br>
                  (<span class="emphasis"><em>Rmath 3.2.3:</em></span> <span class="red">Max = 1.14e+121&#949; (Mean
                  = 3.28e+119&#949;) <a class="link" href="logs.html#errors_GNU_C_version_7_1_0_linux_double_ibeta_inv_Rmath_3_2_3_Inverse_incomplete_beta">And
                  other failures.</a>)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 3.8e+04&#949; (Mean = 2.66e+03&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 4.07e+04&#949; (Mean = 2.86e+03&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 8.59e+03&#949; (Mean = 277&#949;)</span>
                </p>
              </td>
</tr></tbody>
</table></div>
</div>
<br class="table-break"><div class="table">
<a name="math_toolkit.logs_and_tables.all_table.table_ibeta_inva"></a><p class="title"><b>Table&#160;23.57.&#160;Error rates for ibeta_inva</b></p>
<div class="table-contents"><table class="table" summary="Error rates for ibeta_inva">
<colgroup>
<col>
<col>
<col>
<col>
<col>
</colgroup>
<thead><tr>
<th>
              </th>
<th>
                <p>
                  GNU C++ version 7.1.0<br> linux<br> double
                </p>
              </th>
<th>
                <p>
                  GNU C++ version 7.1.0<br> linux<br> long double
                </p>
              </th>
<th>
                <p>
                  Sun compiler version 0x5150<br> Sun Solaris<br> long double
                </p>
              </th>
<th>
                <p>
                  Microsoft Visual C++ version 14.1<br> Win32<br> double
                </p>
              </th>
</tr></thead>
<tbody><tr>
<td>
                <p>
                  Inverse incomplete beta
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 0.602&#949; (Mean = 0.0239&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 377&#949; (Mean = 24.4&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 438&#949; (Mean = 31.3&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 242&#949; (Mean = 22.9&#949;)</span>
                </p>
              </td>
</tr></tbody>
</table></div>
</div>
<br class="table-break"><div class="table">
<a name="math_toolkit.logs_and_tables.all_table.table_ibeta_invb"></a><p class="title"><b>Table&#160;23.58.&#160;Error rates for ibeta_invb</b></p>
<div class="table-contents"><table class="table" summary="Error rates for ibeta_invb">
<colgroup>
<col>
<col>
<col>
<col>
<col>
</colgroup>
<thead><tr>
<th>
              </th>
<th>
                <p>
                  GNU C++ version 7.1.0<br> linux<br> double
                </p>
              </th>
<th>
                <p>
                  GNU C++ version 7.1.0<br> linux<br> long double
                </p>
              </th>
<th>
                <p>
                  Sun compiler version 0x5150<br> Sun Solaris<br> long double
                </p>
              </th>
<th>
                <p>
                  Microsoft Visual C++ version 14.1<br> Win32<br> double
                </p>
              </th>
</tr></thead>
<tbody><tr>
<td>
                <p>
                  Inverse incomplete beta
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 0.765&#949; (Mean = 0.0422&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 407&#949; (Mean = 27.2&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 407&#949; (Mean = 24.4&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 409&#949; (Mean = 19.3&#949;)</span>
                </p>
              </td>
</tr></tbody>
</table></div>
</div>
<br class="table-break"><div class="table">
<a name="math_toolkit.logs_and_tables.all_table.table_ibetac"></a><p class="title"><b>Table&#160;23.59.&#160;Error rates for ibetac</b></p>
<div class="table-contents"><table class="table" summary="Error rates for ibetac">
<colgroup>
<col>
<col>
<col>
<col>
<col>
</colgroup>
<thead><tr>
<th>
              </th>
<th>
                <p>
                  GNU C++ version 7.1.0<br> linux<br> double
                </p>
              </th>
<th>
                <p>
                  GNU C++ version 7.1.0<br> linux<br> long double
                </p>
              </th>
<th>
                <p>
                  Sun compiler version 0x5150<br> Sun Solaris<br> long double
                </p>
              </th>
<th>
                <p>
                  Microsoft Visual C++ version 14.1<br> Win32<br> double
                </p>
              </th>
</tr></thead>
<tbody>
<tr>
<td>
                <p>
                  Incomplete Beta Function: Small Values
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>Rmath
                  3.2.3:</em></span> Max = 22.4&#949; (Mean = 3.67&#949;))
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 10.6&#949; (Mean = 2.22&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 13.8&#949; (Mean = 2.68&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 6.94&#949; (Mean = 1.71&#949;)</span>
                </p>
              </td>
</tr>
<tr>
<td>
                <p>
                  Incomplete Beta Function: Medium Values
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>Rmath
                  3.2.3:</em></span> Max = 204&#949; (Mean = 25.8&#949;))
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 73.9&#949; (Mean = 11.2&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 132&#949; (Mean = 19.8&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 56.7&#949; (Mean = 14.3&#949;)</span>
                </p>
              </td>
</tr>
<tr>
<td>
                <p>
                  Incomplete Beta Function: Large and Diverse Values
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 0.981&#949; (Mean = 0.0573&#949;)</span><br>
                  <br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span> Max = 889&#949; (Mean = 68.4&#949;))
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 3.45e+04&#949; (Mean = 1.32e+03&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 6.31e+04&#949; (Mean = 2.04e+03&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 1.88e+03&#949; (Mean = 82.7&#949;)</span>
                </p>
              </td>
</tr>
<tr>
<td>
                <p>
                  Incomplete Beta Function: Small Integer Values
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>Rmath
                  3.2.3:</em></span> Max = 84.6&#949; (Mean = 18&#949;))
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 5.34&#949; (Mean = 1.11&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 107&#949; (Mean = 17.1&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 6.37&#949; (Mean = 1.03&#949;)</span>
                </p>
              </td>
</tr>
</tbody>
</table></div>
</div>
<br class="table-break"><div class="table">
<a name="math_toolkit.logs_and_tables.all_table.table_ibetac_inv"></a><p class="title"><b>Table&#160;23.60.&#160;Error rates for ibetac_inv</b></p>
<div class="table-contents"><table class="table" summary="Error rates for ibetac_inv">
<colgroup>
<col>
<col>
<col>
<col>
<col>
</colgroup>
<thead><tr>
<th>
              </th>
<th>
                <p>
                  GNU C++ version 7.1.0<br> linux<br> double
                </p>
              </th>
<th>
                <p>
                  GNU C++ version 7.1.0<br> linux<br> long double
                </p>
              </th>
<th>
                <p>
                  Sun compiler version 0x5150<br> Sun Solaris<br> long double
                </p>
              </th>
<th>
                <p>
                  Microsoft Visual C++ version 14.1<br> Win32<br> double
                </p>
              </th>
</tr></thead>
<tbody><tr>
<td>
                <p>
                  Inverse incomplete beta
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 0.977&#949; (Mean = 0.0976&#949;)</span><br>
                  <br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span> <span class="red">Max
                  = 3.01e+132&#949; (Mean = 8.65e+130&#949;) <a class="link" href="logs.html#errors_GNU_C_version_7_1_0_linux_double_ibetac_inv_Rmath_3_2_3_Inverse_incomplete_beta">And
                  other failures.</a>)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 4.88e+04&#949; (Mean = 3.16e+03&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 5.05e+04&#949; (Mean = 3.33e+03&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 2.93e+03&#949; (Mean = 198&#949;)</span>
                </p>
              </td>
</tr></tbody>
</table></div>
</div>
<br class="table-break"><div class="table">
<a name="math_toolkit.logs_and_tables.all_table.table_ibetac_inva"></a><p class="title"><b>Table&#160;23.61.&#160;Error rates for ibetac_inva</b></p>
<div class="table-contents"><table class="table" summary="Error rates for ibetac_inva">
<colgroup>
<col>
<col>
<col>
<col>
<col>
</colgroup>
<thead><tr>
<th>
              </th>
<th>
                <p>
                  GNU C++ version 7.1.0<br> linux<br> double
                </p>
              </th>
<th>
                <p>
                  GNU C++ version 7.1.0<br> linux<br> long double
                </p>
              </th>
<th>
                <p>
                  Sun compiler version 0x5150<br> Sun Solaris<br> long double
                </p>
              </th>
<th>
                <p>
                  Microsoft Visual C++ version 14.1<br> Win32<br> double
                </p>
              </th>
</tr></thead>
<tbody><tr>
<td>
                <p>
                  Inverse incomplete beta
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 0.683&#949; (Mean = 0.0314&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 382&#949; (Mean = 22.2&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 315&#949; (Mean = 23.7&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 408&#949; (Mean = 26.7&#949;)</span>
                </p>
              </td>
</tr></tbody>
</table></div>
</div>
<br class="table-break"><div class="table">
<a name="math_toolkit.logs_and_tables.all_table.table_ibetac_invb"></a><p class="title"><b>Table&#160;23.62.&#160;Error rates for ibetac_invb</b></p>
<div class="table-contents"><table class="table" summary="Error rates for ibetac_invb">
<colgroup>
<col>
<col>
<col>
<col>
<col>
</colgroup>
<thead><tr>
<th>
              </th>
<th>
                <p>
                  GNU C++ version 7.1.0<br> linux<br> double
                </p>
              </th>
<th>
                <p>
                  GNU C++ version 7.1.0<br> linux<br> long double
                </p>
              </th>
<th>
                <p>
                  Sun compiler version 0x5150<br> Sun Solaris<br> long double
                </p>
              </th>
<th>
                <p>
                  Microsoft Visual C++ version 14.1<br> Win32<br> double
                </p>
              </th>
</tr></thead>
<tbody><tr>
<td>
                <p>
                  Inverse incomplete beta
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 0.724&#949; (Mean = 0.0303&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 317&#949; (Mean = 19.8&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 369&#949; (Mean = 22.6&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 271&#949; (Mean = 16.4&#949;)</span>
                </p>
              </td>
</tr></tbody>
</table></div>
</div>
<br class="table-break"><div class="table">
<a name="math_toolkit.logs_and_tables.all_table.table_jacobi_cn"></a><p class="title"><b>Table&#160;23.63.&#160;Error rates for jacobi_cn</b></p>
<div class="table-contents"><table class="table" summary="Error rates for jacobi_cn">
<colgroup>
<col>
<col>
<col>
<col>
<col>
</colgroup>
<thead><tr>
<th>
              </th>
<th>
                <p>
                  GNU C++ version 7.1.0<br> linux<br> double
                </p>
              </th>
<th>
                <p>
                  GNU C++ version 7.1.0<br> linux<br> long double
                </p>
              </th>
<th>
                <p>
                  Sun compiler version 0x5150<br> Sun Solaris<br> long double
                </p>
              </th>
<th>
                <p>
                  Microsoft Visual C++ version 14.1<br> Win32<br> double
                </p>
              </th>
</tr></thead>
<tbody>
<tr>
<td>
                <p>
                  Jacobi Elliptic: Mathworld Data
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
                  2.1:</em></span> Max = 17.3&#949; (Mean = 4.29&#949;) <a class="link" href="logs.html#errors_GNU_C_version_7_1_0_linux_double_jacobi_cn_GSL_2_1_Jacobi_Elliptic_Mathworld_Data">And
                  other failures.</a>)
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 71.6&#949; (Mean = 19.3&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 71.6&#949; (Mean = 19.4&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 45.8&#949; (Mean = 11.4&#949;)</span>
                </p>
              </td>
</tr>
<tr>
<td>
                <p>
                  Jacobi Elliptic: Random Data
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 0.816&#949; (Mean = 0.0563&#949;)</span><br>
                  <br> (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 2.43&#949; (Mean = 0.803&#949;))
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 1.68&#949; (Mean = 0.443&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 1.68&#949; (Mean = 0.454&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 1.83&#949; (Mean = 0.455&#949;)</span>
                </p>
              </td>
</tr>
<tr>
<td>
                <p>
                  Jacobi Elliptic: Random Small Values
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
                  2.1:</em></span> Max = 55.2&#949; (Mean = 1.64&#949;) <a class="link" href="logs.html#errors_GNU_C_version_7_1_0_linux_double_jacobi_cn_GSL_2_1_Jacobi_Elliptic_Random_Small_Values">And
                  other failures.</a>)
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 10.4&#949; (Mean = 0.594&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 10.4&#949; (Mean = 0.602&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 26.2&#949; (Mean = 1.17&#949;)</span>
                </p>
              </td>
</tr>
<tr>
<td>
                <p>
                  Jacobi Elliptic: Modulus near 1
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 0.919&#949; (Mean = 0.127&#949;)</span><br> <br>
                  (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 0&#949; (Mean = 0&#949;) <a class="link" href="logs.html#errors_GNU_C_version_7_1_0_linux_double_jacobi_cn_GSL_2_1_Jacobi_Elliptic_Modulus_near_1">And
                  other failures.</a>)
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 675&#949; (Mean = 87.1&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 675&#949; (Mean = 86.8&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 513&#949; (Mean = 126&#949;)</span>
                </p>
              </td>
</tr>
<tr>
<td>
                <p>
                  Jacobi Elliptic: Large Phi
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 14.2&#949; (Mean = 0.927&#949;)</span><br> <br>
                  (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 5.92e+03&#949; (Mean = 477&#949;))
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 2.97e+04&#949; (Mean = 1.9e+03&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 2.97e+04&#949; (Mean = 1.9e+03&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 3.27e+04&#949; (Mean = 1.93e+03&#949;)</span>
                </p>
              </td>
</tr>
</tbody>
</table></div>
</div>
<br class="table-break"><div class="table">
<a name="math_toolkit.logs_and_tables.all_table.table_jacobi_dn"></a><p class="title"><b>Table&#160;23.64.&#160;Error rates for jacobi_dn</b></p>
<div class="table-contents"><table class="table" summary="Error rates for jacobi_dn">
<colgroup>
<col>
<col>
<col>
<col>
<col>
</colgroup>
<thead><tr>
<th>
              </th>
<th>
                <p>
                  GNU C++ version 7.1.0<br> linux<br> double
                </p>
              </th>
<th>
                <p>
                  GNU C++ version 7.1.0<br> linux<br> long double
                </p>
              </th>
<th>
                <p>
                  Sun compiler version 0x5150<br> Sun Solaris<br> long double
                </p>
              </th>
<th>
                <p>
                  Microsoft Visual C++ version 14.1<br> Win32<br> double
                </p>
              </th>
</tr></thead>
<tbody>
<tr>
<td>
                <p>
                  Jacobi Elliptic: Mathworld Data
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
                  2.1:</em></span> Max = 2.82&#949; (Mean = 1.18&#949;) <a class="link" href="logs.html#errors_GNU_C_version_7_1_0_linux_double_jacobi_dn_GSL_2_1_Jacobi_Elliptic_Mathworld_Data">And
                  other failures.</a>)
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 49&#949; (Mean = 14&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 49&#949; (Mean = 14&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 34.3&#949; (Mean = 8.71&#949;)</span>
                </p>
              </td>
</tr>
<tr>
<td>
                <p>
                  Jacobi Elliptic: Random Data
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
                  2.1:</em></span> Max = 3&#949; (Mean = 0.61&#949;))
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 1.53&#949; (Mean = 0.473&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 1.53&#949; (Mean = 0.481&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 1.52&#949; (Mean = 0.466&#949;)</span>
                </p>
              </td>
</tr>
<tr>
<td>
                <p>
                  Jacobi Elliptic: Random Small Values
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 0.5&#949; (Mean = 0.0122&#949;)</span><br> <br>
                  (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 1.5&#949; (Mean = 0.391&#949;) <a class="link" href="logs.html#errors_GNU_C_version_7_1_0_linux_double_jacobi_dn_GSL_2_1_Jacobi_Elliptic_Random_Small_Values">And
                  other failures.</a>)
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 22.4&#949; (Mean = 0.777&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 22.4&#949; (Mean = 0.763&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 16.1&#949; (Mean = 0.685&#949;)</span>
                </p>
              </td>
</tr>
<tr>
<td>
                <p>
                  Jacobi Elliptic: Modulus near 1
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 2.28&#949; (Mean = 0.194&#949;)</span><br> <br>
                  (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 0&#949; (Mean = 0&#949;) <a class="link" href="logs.html#errors_GNU_C_version_7_1_0_linux_double_jacobi_dn_GSL_2_1_Jacobi_Elliptic_Modulus_near_1">And
                  other failures.</a>)
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 3.75e+03&#949; (Mean = 293&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 3.75e+03&#949; (Mean = 293&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 6.24e+03&#949; (Mean = 482&#949;)</span>
                </p>
              </td>
</tr>
<tr>
<td>
                <p>
                  Jacobi Elliptic: Large Phi
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 14.1&#949; (Mean = 0.897&#949;)</span><br> <br>
                  (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 121&#949; (Mean = 22&#949;))
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 2.82e+04&#949; (Mean = 1.79e+03&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 2.82e+04&#949; (Mean = 1.79e+03&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 1.67e+04&#949; (Mean = 1e+03&#949;)</span>
                </p>
              </td>
</tr>
</tbody>
</table></div>
</div>
<br class="table-break"><div class="table">
<a name="math_toolkit.logs_and_tables.all_table.table_jacobi_sn"></a><p class="title"><b>Table&#160;23.65.&#160;Error rates for jacobi_sn</b></p>
<div class="table-contents"><table class="table" summary="Error rates for jacobi_sn">
<colgroup>
<col>
<col>
<col>
<col>
<col>
</colgroup>
<thead><tr>
<th>
              </th>
<th>
                <p>
                  GNU C++ version 7.1.0<br> linux<br> double
                </p>
              </th>
<th>
                <p>
                  GNU C++ version 7.1.0<br> linux<br> long double
                </p>
              </th>
<th>
                <p>
                  Sun compiler version 0x5150<br> Sun Solaris<br> long double
                </p>
              </th>
<th>
                <p>
                  Microsoft Visual C++ version 14.1<br> Win32<br> double
                </p>
              </th>
</tr></thead>
<tbody>
<tr>
<td>
                <p>
                  Jacobi Elliptic: Mathworld Data
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
                  2.1:</em></span> Max = 588&#949; (Mean = 146&#949;) <a class="link" href="logs.html#errors_GNU_C_version_7_1_0_linux_double_jacobi_sn_GSL_2_1_Jacobi_Elliptic_Mathworld_Data">And
                  other failures.</a>)
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 341&#949; (Mean = 80.7&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 341&#949; (Mean = 80.7&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 481&#949; (Mean = 113&#949;)</span>
                </p>
              </td>
</tr>
<tr>
<td>
                <p>
                  Jacobi Elliptic: Random Data
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
                  2.1:</em></span> Max = 4.02&#949; (Mean = 1.07&#949;))
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 2.01&#949; (Mean = 0.584&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 2.01&#949; (Mean = 0.593&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 1.92&#949; (Mean = 0.567&#949;)</span>
                </p>
              </td>
</tr>
<tr>
<td>
                <p>
                  Jacobi Elliptic: Random Small Values
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
                  2.1:</em></span> Max = 11.7&#949; (Mean = 1.65&#949;) <a class="link" href="logs.html#errors_GNU_C_version_7_1_0_linux_double_jacobi_sn_GSL_2_1_Jacobi_Elliptic_Random_Small_Values">And
                  other failures.</a>)
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 1.99&#949; (Mean = 0.347&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 1.99&#949; (Mean = 0.347&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 2.11&#949; (Mean = 0.385&#949;)</span>
                </p>
              </td>
</tr>
<tr>
<td>
                <p>
                  Jacobi Elliptic: Modulus near 1
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
                  2.1:</em></span> Max = 0&#949; (Mean = 0&#949;) <a class="link" href="logs.html#errors_GNU_C_version_7_1_0_linux_double_jacobi_sn_GSL_2_1_Jacobi_Elliptic_Modulus_near_1">And
                  other failures.</a>)
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 109&#949; (Mean = 7.35&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 109&#949; (Mean = 7.38&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 23.2&#949; (Mean = 1.85&#949;)</span>
                </p>
              </td>
</tr>
<tr>
<td>
                <p>
                  Jacobi Elliptic: Large Phi
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 12&#949; (Mean = 0.771&#949;)</span><br> <br>
                  (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 4.54e+04&#949; (Mean = 2.63e+03&#949;))
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 2.45e+04&#949; (Mean = 1.51e+03&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 2.45e+04&#949; (Mean = 1.51e+03&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 4.36e+04&#949; (Mean = 2.54e+03&#949;)</span>
                </p>
              </td>
</tr>
</tbody>
</table></div>
</div>
<br class="table-break"><div class="table">
<a name="math_toolkit.logs_and_tables.all_table.table_jacobi_zeta"></a><p class="title"><b>Table&#160;23.66.&#160;Error rates for jacobi_zeta</b></p>
<div class="table-contents"><table class="table" summary="Error rates for jacobi_zeta">
<colgroup>
<col>
<col>
<col>
<col>
<col>
</colgroup>
<thead><tr>
<th>
              </th>
<th>
                <p>
                  GNU C++ version 7.1.0<br> linux<br> double
                </p>
              </th>
<th>
                <p>
                  GNU C++ version 7.1.0<br> linux<br> long double
                </p>
              </th>
<th>
                <p>
                  Sun compiler version 0x5150<br> Sun Solaris<br> long double
                </p>
              </th>
<th>
                <p>
                  Microsoft Visual C++ version 14.1<br> Win32<br> double
                </p>
              </th>
</tr></thead>
<tbody>
<tr>
<td>
                <p>
                  Elliptic Integral Jacobi Zeta: Mathworld Data
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 1.66&#949; (Mean = 0.48&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 1.66&#949; (Mean = 0.48&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 1.52&#949; (Mean = 0.357&#949;)</span>
                </p>
              </td>
</tr>
<tr>
<td>
                <p>
                  Elliptic Integral Jacobi Zeta: Random Data
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 2.99&#949; (Mean = 0.824&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 3.96&#949; (Mean = 1.06&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 3.89&#949; (Mean = 0.824&#949;)</span>
                </p>
              </td>
</tr>
<tr>
<td>
                <p>
                  Elliptic Integral Jacobi Zeta: Large Phi Values
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 2.92&#949; (Mean = 0.951&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 3.05&#949; (Mean = 1.13&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 2.52&#949; (Mean = 0.977&#949;)</span>
                </p>
              </td>
</tr>
</tbody>
</table></div>
</div>
<br class="table-break"><div class="table">
<a name="math_toolkit.logs_and_tables.all_table.table_laguerre_n_m_x_"></a><p class="title"><b>Table&#160;23.67.&#160;Error rates for laguerre(n, m, x)</b></p>
<div class="table-contents"><table class="table" summary="Error rates for laguerre(n, m, x)">
<colgroup>
<col>
<col>
<col>
<col>
<col>
</colgroup>
<thead><tr>
<th>
              </th>
<th>
                <p>
                  GNU C++ version 7.1.0<br> linux<br> double
                </p>
              </th>
<th>
                <p>
                  GNU C++ version 7.1.0<br> linux<br> long double
                </p>
              </th>
<th>
                <p>
                  Sun compiler version 0x5150<br> Sun Solaris<br> long double
                </p>
              </th>
<th>
                <p>
                  Microsoft Visual C++ version 14.1<br> Win32<br> double
                </p>
              </th>
</tr></thead>
<tbody><tr>
<td>
                <p>
                  Associated Laguerre Polynomials
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 0.84&#949; (Mean = 0.0358&#949;)</span><br> <br>
                  (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 434&#949; (Mean = 10.7&#949;))
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 167&#949; (Mean = 6.38&#949;)</span><br> <br>
                  (<span class="emphasis"><em>&lt;cmath&gt;:</em></span> Max = 206&#949; (Mean = 6.86&#949;))
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 167&#949; (Mean = 6.38&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 434&#949; (Mean = 11.1&#949;)</span>
                </p>
              </td>
</tr></tbody>
</table></div>
</div>
<br class="table-break"><div class="table">
<a name="math_toolkit.logs_and_tables.all_table.table_laguerre_n_x_"></a><p class="title"><b>Table&#160;23.68.&#160;Error rates for laguerre(n, x)</b></p>
<div class="table-contents"><table class="table" summary="Error rates for laguerre(n, x)">
<colgroup>
<col>
<col>
<col>
<col>
<col>
</colgroup>
<thead><tr>
<th>
              </th>
<th>
                <p>
                  GNU C++ version 7.1.0<br> linux<br> double
                </p>
              </th>
<th>
                <p>
                  GNU C++ version 7.1.0<br> linux<br> long double
                </p>
              </th>
<th>
                <p>
                  Sun compiler version 0x5150<br> Sun Solaris<br> long double
                </p>
              </th>
<th>
                <p>
                  Microsoft Visual C++ version 14.1<br> Win32<br> double
                </p>
              </th>
</tr></thead>
<tbody><tr>
<td>
                <p>
                  Laguerre Polynomials
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 6.82&#949; (Mean = 0.408&#949;)</span><br> <br>
                  (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 3.1e+03&#949; (Mean = 185&#949;))
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 1.39e+04&#949; (Mean = 828&#949;)</span><br>
                  <br> (<span class="emphasis"><em>&lt;cmath&gt;:</em></span> Max = 4.2e+03&#949; (Mean
                  = 251&#949;))
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 1.39e+04&#949; (Mean = 828&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 3.1e+03&#949; (Mean = 185&#949;)</span>
                </p>
              </td>
</tr></tbody>
</table></div>
</div>
<br class="table-break"><div class="table">
<a name="math_toolkit.logs_and_tables.all_table.table_legendre_p"></a><p class="title"><b>Table&#160;23.69.&#160;Error rates for legendre_p</b></p>
<div class="table-contents"><table class="table" summary="Error rates for legendre_p">
<colgroup>
<col>
<col>
<col>
<col>
<col>
</colgroup>
<thead><tr>
<th>
              </th>
<th>
                <p>
                  GNU C++ version 7.1.0<br> linux<br> double
                </p>
              </th>
<th>
                <p>
                  GNU C++ version 7.1.0<br> linux<br> long double
                </p>
              </th>
<th>
                <p>
                  Sun compiler version 0x5150<br> Sun Solaris<br> long double
                </p>
              </th>
<th>
                <p>
                  Microsoft Visual C++ version 14.1<br> Win32<br> double
                </p>
              </th>
</tr></thead>
<tbody>
<tr>
<td>
                <p>
                  Legendre Polynomials: Small Values
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 0.732&#949; (Mean = 0.0619&#949;)</span><br>
                  <br> (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 211&#949; (Mean = 20.4&#949;))
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 69.2&#949; (Mean = 9.58&#949;)</span><br> <br>
                  (<span class="emphasis"><em>&lt;cmath&gt;:</em></span> Max = 124&#949; (Mean = 13.2&#949;))
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 69.2&#949; (Mean = 9.58&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 211&#949; (Mean = 20.4&#949;)</span>
                </p>
              </td>
</tr>
<tr>
<td>
                <p>
                  Legendre Polynomials: Large Values
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 0.632&#949; (Mean = 0.0693&#949;)</span><br>
                  <br> (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 300&#949; (Mean = 33.2&#949;))
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 699&#949; (Mean = 59.6&#949;)</span><br> <br>
                  (<span class="emphasis"><em>&lt;cmath&gt;:</em></span> Max = 343&#949; (Mean = 32.1&#949;))
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 699&#949; (Mean = 59.6&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 300&#949; (Mean = 33.2&#949;)</span>
                </p>
              </td>
</tr>
</tbody>
</table></div>
</div>
<br class="table-break"><div class="table">
<a name="math_toolkit.logs_and_tables.all_table.table_legendre_p_associated_"></a><p class="title"><b>Table&#160;23.70.&#160;Error rates for legendre_p (associated)</b></p>
<div class="table-contents"><table class="table" summary="Error rates for legendre_p (associated)">
<colgroup>
<col>
<col>
<col>
<col>
<col>
</colgroup>
<thead><tr>
<th>
              </th>
<th>
                <p>
                  GNU C++ version 7.1.0<br> linux<br> double
                </p>
              </th>
<th>
                <p>
                  GNU C++ version 7.1.0<br> linux<br> long double
                </p>
              </th>
<th>
                <p>
                  Sun compiler version 0x5150<br> Sun Solaris<br> long double
                </p>
              </th>
<th>
                <p>
                  Microsoft Visual C++ version 14.1<br> Win32<br> double
                </p>
              </th>
</tr></thead>
<tbody><tr>
<td>
                <p>
                  Associated Legendre Polynomials: Small Values
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 0.999&#949; (Mean = 0.05&#949;)</span><br> <br>
                  (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 121&#949; (Mean = 6.75&#949;) <a class="link" href="logs.html#errors_GNU_C_version_7_1_0_linux_double_legendre_p_associated__GSL_2_1_Associated_Legendre_Polynomials_Small_Values">And
                  other failures.</a>)
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 175&#949; (Mean = 9.88&#949;)</span><br> <br>
                  (<span class="emphasis"><em>&lt;cmath&gt;:</em></span> Max = 175&#949; (Mean = 9.36&#949;) <a class="link" href="logs.html#errors_GNU_C_version_7_1_0_linux_long_double_legendre_p_associated___cmath__Associated_Legendre_Polynomials_Small_Values">And
                  other failures.</a>)
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 77.7&#949; (Mean = 5.59&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 121&#949; (Mean = 7.14&#949;)</span>
                </p>
              </td>
</tr></tbody>
</table></div>
</div>
<br class="table-break"><div class="table">
<a name="math_toolkit.logs_and_tables.all_table.table_legendre_q"></a><p class="title"><b>Table&#160;23.71.&#160;Error rates for legendre_q</b></p>
<div class="table-contents"><table class="table" summary="Error rates for legendre_q">
<colgroup>
<col>
<col>
<col>
<col>
<col>
</colgroup>
<thead><tr>
<th>
              </th>
<th>
                <p>
                  GNU C++ version 7.1.0<br> linux<br> double
                </p>
              </th>
<th>
                <p>
                  GNU C++ version 7.1.0<br> linux<br> long double
                </p>
              </th>
<th>
                <p>
                  Sun compiler version 0x5150<br> Sun Solaris<br> long double
                </p>
              </th>
<th>
                <p>
                  Microsoft Visual C++ version 14.1<br> Win32<br> double
                </p>
              </th>
</tr></thead>
<tbody>
<tr>
<td>
                <p>
                  Legendre Polynomials: Small Values
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 0.612&#949; (Mean = 0.0517&#949;)</span><br>
                  <br> (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 46.4&#949; (Mean = 7.46&#949;))
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 50.9&#949; (Mean = 9&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 50.9&#949; (Mean = 8.98&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 46.4&#949; (Mean = 7.32&#949;)</span>
                </p>
              </td>
</tr>
<tr>
<td>
                <p>
                  Legendre Polynomials: Large Values
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 2.49&#949; (Mean = 0.202&#949;)</span><br> <br>
                  (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 4.6e+03&#949; (Mean = 366&#949;))
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 5.98e+03&#949; (Mean = 478&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 5.98e+03&#949; (Mean = 478&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 4.6e+03&#949; (Mean = 366&#949;)</span>
                </p>
              </td>
</tr>
</tbody>
</table></div>
</div>
<br class="table-break"><div class="table">
<a name="math_toolkit.logs_and_tables.all_table.table_lgamma"></a><p class="title"><b>Table&#160;23.72.&#160;Error rates for lgamma</b></p>
<div class="table-contents"><table class="table" summary="Error rates for lgamma">
<colgroup>
<col>
<col>
<col>
<col>
<col>
</colgroup>
<thead><tr>
<th>
              </th>
<th>
                <p>
                  GNU C++ version 7.1.0<br> linux<br> double
                </p>
              </th>
<th>
                <p>
                  GNU C++ version 7.1.0<br> linux<br> long double
                </p>
              </th>
<th>
                <p>
                  Sun compiler version 0x5150<br> Sun Solaris<br> long double
                </p>
              </th>
<th>
                <p>
                  Microsoft Visual C++ version 14.1<br> Win32<br> double
                </p>
              </th>
</tr></thead>
<tbody>
<tr>
<td>
                <p>
                  factorials
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
                  2.1:</em></span> Max = 33.6&#949; (Mean = 2.78&#949;))<br> (<span class="emphasis"><em>Rmath
                  3.2.3:</em></span> Max = 1.55&#949; (Mean = 0.592&#949;))
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 0.991&#949; (Mean = 0.308&#949;)</span><br> <br>
                  (<span class="emphasis"><em>&lt;cmath&gt;:</em></span> Max = 1.67&#949; (Mean = 0.487&#949;))<br>
                  (<span class="emphasis"><em>&lt;math.h&gt;:</em></span> Max = 1.67&#949; (Mean = 0.487&#949;))
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 0.991&#949; (Mean = 0.383&#949;)</span><br> <br>
                  (<span class="emphasis"><em>&lt;math.h&gt;:</em></span> Max = 1.36&#949; (Mean = 0.476&#949;))
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 0.914&#949; (Mean = 0.175&#949;)</span><br> <br>
                  (<span class="emphasis"><em>&lt;math.h&gt;:</em></span> Max = 0.958&#949; (Mean = 0.38&#949;))
                </p>
              </td>
</tr>
<tr>
<td>
                <p>
                  near 0
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
                  2.1:</em></span> Max = 5.21&#949; (Mean = 1.57&#949;))<br> (<span class="emphasis"><em>Rmath
                  3.2.3:</em></span> Max = 0&#949; (Mean = 0&#949;))
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 1.42&#949; (Mean = 0.566&#949;)</span><br> <br>
                  (<span class="emphasis"><em>&lt;cmath&gt;:</em></span> Max = 0.964&#949; (Mean = 0.543&#949;))<br>
                  (<span class="emphasis"><em>&lt;math.h&gt;:</em></span> Max = 0.964&#949; (Mean = 0.543&#949;))
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 1.42&#949; (Mean = 0.566&#949;)</span><br> <br>
                  (<span class="emphasis"><em>&lt;math.h&gt;:</em></span> Max = 0.964&#949; (Mean = 0.543&#949;))
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 0.964&#949; (Mean = 0.462&#949;)</span><br> <br>
                  (<span class="emphasis"><em>&lt;math.h&gt;:</em></span> Max = 0.962&#949; (Mean = 0.372&#949;))
                </p>
              </td>
</tr>
<tr>
<td>
                <p>
                  near 1
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
                  2.1:</em></span> Max = 442&#949; (Mean = 88.8&#949;))<br> (<span class="emphasis"><em>Rmath
                  3.2.3:</em></span> Max = 7.99e+04&#949; (Mean = 1.68e+04&#949;))
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 0.948&#949; (Mean = 0.36&#949;)</span><br> <br>
                  (<span class="emphasis"><em>&lt;cmath&gt;:</em></span> Max = 0.615&#949; (Mean = 0.096&#949;))<br>
                  (<span class="emphasis"><em>&lt;math.h&gt;:</em></span> Max = 0.615&#949; (Mean = 0.096&#949;))
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 0.948&#949; (Mean = 0.36&#949;)</span><br> <br>
                  (<span class="emphasis"><em>&lt;math.h&gt;:</em></span> Max = 1.71&#949; (Mean = 0.581&#949;))
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 0.867&#949; (Mean = 0.468&#949;)</span><br> <br>
                  (<span class="emphasis"><em>&lt;math.h&gt;:</em></span> Max = 0.906&#949; (Mean = 0.565&#949;))
                </p>
              </td>
</tr>
<tr>
<td>
                <p>
                  near 2
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
                  2.1:</em></span> Max = 1.17e+03&#949; (Mean = 274&#949;))<br> (<span class="emphasis"><em>Rmath
                  3.2.3:</em></span> Max = 2.63e+05&#949; (Mean = 5.84e+04&#949;))
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 0.878&#949; (Mean = 0.242&#949;)</span><br> <br>
                  (<span class="emphasis"><em>&lt;cmath&gt;:</em></span> Max = 0.741&#949; (Mean = 0.263&#949;))<br>
                  (<span class="emphasis"><em>&lt;math.h&gt;:</em></span> Max = 0.741&#949; (Mean = 0.263&#949;))
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 0.878&#949; (Mean = 0.242&#949;)</span><br> <br>
                  (<span class="emphasis"><em>&lt;math.h&gt;:</em></span> Max = 0.598&#949; (Mean = 0.235&#949;))
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 0.591&#949; (Mean = 0.159&#949;)</span><br> <br>
                  (<span class="emphasis"><em>&lt;math.h&gt;:</em></span> Max = 0.741&#949; (Mean = 0.473&#949;))
                </p>
              </td>
</tr>
<tr>
<td>
                <p>
                  near -10
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
                  2.1:</em></span> Max = 24.9&#949; (Mean = 4.6&#949;))<br> (<span class="emphasis"><em>Rmath
                  3.2.3:</em></span> Max = 4.22&#949; (Mean = 1.26&#949;))
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 3.81&#949; (Mean = 1.01&#949;)</span><br> <br>
                  (<span class="emphasis"><em>&lt;cmath&gt;:</em></span> Max = 0.997&#949; (Mean = 0.412&#949;))<br>
                  (<span class="emphasis"><em>&lt;math.h&gt;:</em></span> Max = 0.997&#949; (Mean = 0.412&#949;))
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 3.81&#949; (Mean = 1.01&#949;)</span><br> <br>
                  (<span class="emphasis"><em>&lt;math.h&gt;:</em></span> Max = 3.04&#949; (Mean = 1.01&#949;))
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 4.22&#949; (Mean = 1.33&#949;)</span><br> <br>
                  (<span class="emphasis"><em>&lt;math.h&gt;:</em></span> Max = 0.997&#949; (Mean = 0.444&#949;))
                </p>
              </td>
</tr>
<tr>
<td>
                <p>
                  near -55
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
                  2.1:</em></span> Max = 7.02&#949; (Mean = 1.47&#949;))<br> (<span class="emphasis"><em>Rmath
                  3.2.3:</em></span> Max = 250&#949; (Mean = 60.9&#949;))
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 0.821&#949; (Mean = 0.513&#949;)</span><br> <br>
                  (<span class="emphasis"><em>&lt;cmath&gt;:</em></span> Max = 1.58&#949; (Mean = 0.672&#949;))<br>
                  (<span class="emphasis"><em>&lt;math.h&gt;:</em></span> Max = 1.58&#949; (Mean = 0.672&#949;))
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 1.59&#949; (Mean = 0.587&#949;)</span><br> <br>
                  (<span class="emphasis"><em>&lt;math.h&gt;:</em></span> Max = 0.821&#949; (Mean = 0.674&#949;))
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 0.821&#949; (Mean = 0.419&#949;)</span><br> <br>
                  (<span class="emphasis"><em>&lt;math.h&gt;:</em></span> Max = 249&#949; (Mean = 43.1&#949;))
                </p>
              </td>
</tr>
</tbody>
</table></div>
</div>
<br class="table-break"><div class="table">
<a name="math_toolkit.logs_and_tables.all_table.table_log1p"></a><p class="title"><b>Table&#160;23.73.&#160;Error rates for log1p</b></p>
<div class="table-contents"><table class="table" summary="Error rates for log1p">
<colgroup>
<col>
<col>
<col>
<col>
<col>
</colgroup>
<thead><tr>
<th>
              </th>
<th>
                <p>
                  GNU C++ version 7.1.0<br> linux<br> long double
                </p>
              </th>
<th>
                <p>
                  GNU C++ version 7.1.0<br> linux<br> double
                </p>
              </th>
<th>
                <p>
                  Sun compiler version 0x5150<br> Sun Solaris<br> long double
                </p>
              </th>
<th>
                <p>
                  Microsoft Visual C++ version 14.1<br> Win32<br> double
                </p>
              </th>
</tr></thead>
<tbody><tr>
<td>
                <p>
                  Random test data
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 0.818&#949; (Mean = 0.227&#949;)</span><br> <br>
                  (<span class="emphasis"><em>&lt;cmath&gt;:</em></span> Max = 0.818&#949; (Mean = 0.227&#949;))<br>
                  (<span class="emphasis"><em>&lt;math.h&gt;:</em></span> Max = 0.818&#949; (Mean = 0.227&#949;))
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 0.846&#949; (Mean = 0.153&#949;)</span><br> <br>
                  (<span class="emphasis"><em>Rmath 3.2.3:</em></span> Max = 0.846&#949; (Mean = 0.153&#949;))
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 2.3&#949; (Mean = 0.66&#949;)</span><br> <br>
                  (<span class="emphasis"><em>&lt;math.h&gt;:</em></span> Max = 0.818&#949; (Mean = 0.249&#949;))
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 0.509&#949; (Mean = 0.057&#949;)</span><br> <br>
                  (<span class="emphasis"><em>&lt;math.h&gt;:</em></span> Max = 0.509&#949; (Mean = 0.057&#949;))
                </p>
              </td>
</tr></tbody>
</table></div>
</div>
<br class="table-break"><div class="table">
<a name="math_toolkit.logs_and_tables.all_table.table_non_central_beta_CDF"></a><p class="title"><b>Table&#160;23.74.&#160;Error rates for non central beta CDF</b></p>
<div class="table-contents"><table class="table" summary="Error rates for non central beta CDF">
<colgroup>
<col>
<col>
<col>
<col>
<col>
</colgroup>
<thead><tr>
<th>
              </th>
<th>
                <p>
                  GNU C++ version 7.1.0<br> linux<br> double
                </p>
              </th>
<th>
                <p>
                  GNU C++ version 7.1.0<br> linux<br> long double
                </p>
              </th>
<th>
                <p>
                  Sun compiler version 0x5150<br> Sun Solaris<br> long double
                </p>
              </th>
<th>
                <p>
                  Microsoft Visual C++ version 14.1<br> Win32<br> double
                </p>
              </th>
</tr></thead>
<tbody>
<tr>
<td>
                <p>
                  Non Central Beta, medium parameters
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 0.998&#949; (Mean = 0.0649&#949;)</span><br>
                  <br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span> <span class="red">Max
                  = 1.46e+26&#949; (Mean = 3.5e+24&#949;) <a class="link" href="logs.html#errors_GNU_C_version_7_1_0_linux_double_non_central_beta_CDF_Rmath_3_2_3_Non_Central_Beta_medium_parameters">And
                  other failures.</a>)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 824&#949; (Mean = 27.4&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 832&#949; (Mean = 38.1&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 242&#949; (Mean = 31&#949;)</span>
                </p>
              </td>
</tr>
<tr>
<td>
                <p>
                  Non Central Beta, large parameters
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 1.18&#949; (Mean = 0.175&#949;)</span><br> <br>
                  (<span class="emphasis"><em>Rmath 3.2.3:</em></span> <span class="red">Max = 1.01e+36&#949; (Mean
                  = 1.19e+35&#949;) <a class="link" href="logs.html#errors_GNU_C_version_7_1_0_linux_double_non_central_beta_CDF_Rmath_3_2_3_Non_Central_Beta_large_parameters">And
                  other failures.</a>)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 2.5e+04&#949; (Mean = 3.78e+03&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 2.57e+04&#949; (Mean = 4.45e+03&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 3.66e+03&#949; (Mean = 500&#949;)</span>
                </p>
              </td>
</tr>
</tbody>
</table></div>
</div>
<br class="table-break"><div class="table">
<a name="math_toolkit.logs_and_tables.all_table.table_non_central_beta_CDF_complement"></a><p class="title"><b>Table&#160;23.75.&#160;Error rates for non central beta CDF complement</b></p>
<div class="table-contents"><table class="table" summary="Error rates for non central beta CDF complement">
<colgroup>
<col>
<col>
<col>
<col>
<col>
</colgroup>
<thead><tr>
<th>
              </th>
<th>
                <p>
                  GNU C++ version 7.1.0<br> linux<br> double
                </p>
              </th>
<th>
                <p>
                  GNU C++ version 7.1.0<br> linux<br> long double
                </p>
              </th>
<th>
                <p>
                  Sun compiler version 0x5150<br> Sun Solaris<br> long double
                </p>
              </th>
<th>
                <p>
                  Microsoft Visual C++ version 14.1<br> Win32<br> double
                </p>
              </th>
</tr></thead>
<tbody>
<tr>
<td>
                <p>
                  Non Central Beta, medium parameters
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 0.998&#949; (Mean = 0.0936&#949;)</span><br>
                  <br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span> <span class="red">Max
                  = 7.5e+97&#949; (Mean = 1.37e+96&#949;) <a class="link" href="logs.html#errors_GNU_C_version_7_1_0_linux_double_non_central_beta_CDF_complement_Rmath_3_2_3_Non_Central_Beta_medium_parameters">And
                  other failures.</a>)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 396&#949; (Mean = 50.7&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 554&#949; (Mean = 57.2&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 624&#949; (Mean = 62.7&#949;)</span>
                </p>
              </td>
</tr>
<tr>
<td>
                <p>
                  Non Central Beta, large parameters
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 0.986&#949; (Mean = 0.188&#949;)</span><br> <br>
                  (<span class="emphasis"><em>Rmath 3.2.3:</em></span> <span class="red">Max = +INF&#949; (Mean
                  = +INF&#949;) <a class="link" href="logs.html#errors_GNU_C_version_7_1_0_linux_double_non_central_beta_CDF_complement_Rmath_3_2_3_Non_Central_Beta_large_parameters">And
                  other failures.</a>)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 6.83e+03&#949; (Mean = 993&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 3.56e+03&#949; (Mean = 707&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 1.25e+04&#949; (Mean = 1.49e+03&#949;)</span>
                </p>
              </td>
</tr>
</tbody>
</table></div>
</div>
<br class="table-break"><div class="table">
<a name="math_toolkit.logs_and_tables.all_table.table_non_central_chi_squared_CDF"></a><p class="title"><b>Table&#160;23.76.&#160;Error rates for non central chi squared CDF</b></p>
<div class="table-contents"><table class="table" summary="Error rates for non central chi squared CDF">
<colgroup>
<col>
<col>
<col>
<col>
<col>
</colgroup>
<thead><tr>
<th>
              </th>
<th>
                <p>
                  GNU C++ version 7.1.0<br> linux<br> double
                </p>
              </th>
<th>
                <p>
                  GNU C++ version 7.1.0<br> linux<br> long double
                </p>
              </th>
<th>
                <p>
                  Sun compiler version 0x5150<br> Sun Solaris<br> long double
                </p>
              </th>
<th>
                <p>
                  Microsoft Visual C++ version 14.1<br> Win32<br> double
                </p>
              </th>
</tr></thead>
<tbody>
<tr>
<td>
                <p>
                  Non Central Chi Squared, medium parameters
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 0.99&#949; (Mean = 0.0544&#949;)</span><br> <br>
                  (<span class="emphasis"><em>Rmath 3.2.3:</em></span> Max = 727&#949; (Mean = 121&#949;))
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 46.5&#949; (Mean = 10.3&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 115&#949; (Mean = 13.9&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 48.9&#949; (Mean = 10&#949;)</span>
                </p>
              </td>
</tr>
<tr>
<td>
                <p>
                  Non Central Chi Squared, large parameters
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 1.07&#949; (Mean = 0.102&#949;)</span><br> <br>
                  (<span class="emphasis"><em>Rmath 3.2.3:</em></span> <span class="red">Max = 3.27e+08&#949; (Mean
                  = 2.23e+07&#949;))</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 3.07e+03&#949; (Mean = 336&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 6.17e+03&#949; (Mean = 677&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 9.79e+03&#949; (Mean = 723&#949;)</span>
                </p>
              </td>
</tr>
</tbody>
</table></div>
</div>
<br class="table-break"><div class="table">
<a name="math_toolkit.logs_and_tables.all_table.table_non_central_chi_squared_CDF_complement"></a><p class="title"><b>Table&#160;23.77.&#160;Error rates for non central chi squared CDF complement</b></p>
<div class="table-contents"><table class="table" summary="Error rates for non central chi squared CDF complement">
<colgroup>
<col>
<col>
<col>
<col>
<col>
</colgroup>
<thead><tr>
<th>
              </th>
<th>
                <p>
                  GNU C++ version 7.1.0<br> linux<br> double
                </p>
              </th>
<th>
                <p>
                  GNU C++ version 7.1.0<br> linux<br> long double
                </p>
              </th>
<th>
                <p>
                  Sun compiler version 0x5150<br> Sun Solaris<br> long double
                </p>
              </th>
<th>
                <p>
                  Microsoft Visual C++ version 14.1<br> Win32<br> double
                </p>
              </th>
</tr></thead>
<tbody>
<tr>
<td>
                <p>
                  Non Central Chi Squared, medium parameters
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 0.96&#949; (Mean = 0.0635&#949;)</span><br> <br>
                  (<span class="emphasis"><em>Rmath 3.2.3:</em></span> <span class="red">Max = +INF&#949; (Mean
                  = +INF&#949;) <a class="link" href="logs.html#errors_GNU_C_version_7_1_0_linux_double_non_central_chi_squared_CDF_complement_Rmath_3_2_3_Non_Central_Chi_Squared_medium_parameters">And
                  other failures.</a>)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 107&#949; (Mean = 17.2&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 171&#949; (Mean = 22.8&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 98.6&#949; (Mean = 15.8&#949;)</span>
                </p>
              </td>
</tr>
<tr>
<td>
                <p>
                  Non Central Chi Squared, large parameters
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 2.11&#949; (Mean = 0.278&#949;)</span><br> <br>
                  (<span class="emphasis"><em>Rmath 3.2.3:</em></span> <span class="red">Max = +INF&#949; (Mean
                  = +INF&#949;) <a class="link" href="logs.html#errors_GNU_C_version_7_1_0_linux_double_non_central_chi_squared_CDF_complement_Rmath_3_2_3_Non_Central_Chi_Squared_large_parameters">And
                  other failures.</a>)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 5.02e+03&#949; (Mean = 630&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 5.1e+03&#949; (Mean = 577&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 5.43e+03&#949; (Mean = 705&#949;)</span>
                </p>
              </td>
</tr>
</tbody>
</table></div>
</div>
<br class="table-break"><div class="table">
<a name="math_toolkit.logs_and_tables.all_table.table_non_central_t_CDF"></a><p class="title"><b>Table&#160;23.78.&#160;Error rates for non central t CDF</b></p>
<div class="table-contents"><table class="table" summary="Error rates for non central t CDF">
<colgroup>
<col>
<col>
<col>
<col>
<col>
</colgroup>
<thead><tr>
<th>
              </th>
<th>
                <p>
                  GNU C++ version 7.1.0<br> linux<br> double
                </p>
              </th>
<th>
                <p>
                  GNU C++ version 7.1.0<br> linux<br> long double
                </p>
              </th>
<th>
                <p>
                  Sun compiler version 0x5150<br> Sun Solaris<br> long double
                </p>
              </th>
<th>
                <p>
                  Microsoft Visual C++ version 14.1<br> Win32<br> double
                </p>
              </th>
</tr></thead>
<tbody>
<tr>
<td>
                <p>
                  Non Central T
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 0.796&#949; (Mean = 0.0691&#949;)</span><br>
                  <br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span> <span class="red">Max
                  = 5.28e+15&#949; (Mean = 8.49e+14&#949;) <a class="link" href="logs.html#errors_GNU_C_version_7_1_0_linux_double_non_central_t_CDF_Rmath_3_2_3_Non_Central_T">And
                  other failures.</a>)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 139&#949; (Mean = 31&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 145&#949; (Mean = 30.9&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 135&#949; (Mean = 32.1&#949;)</span>
                </p>
              </td>
</tr>
<tr>
<td>
                <p>
                  Non Central T (small non-centrality)
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>Rmath
                  3.2.3:</em></span> Max = 2.09e+03&#949; (Mean = 244&#949;))
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 3.86&#949; (Mean = 1.4&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 9.15&#949; (Mean = 2.13&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 6.17&#949; (Mean = 1.45&#949;)</span>
                </p>
              </td>
</tr>
<tr>
<td>
                <p>
                  Non Central T (large parameters)
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 257&#949; (Mean = 72.1&#949;)</span><br> <br>
                  (<span class="emphasis"><em>Rmath 3.2.3:</em></span> Max = 2.46&#949; (Mean = 0.657&#949;))
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 5.26e+05&#949; (Mean = 1.48e+05&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 5.24e+05&#949; (Mean = 1.47e+05&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 286&#949; (Mean = 62.8&#949;)</span>
                </p>
              </td>
</tr>
</tbody>
</table></div>
</div>
<br class="table-break"><div class="table">
<a name="math_toolkit.logs_and_tables.all_table.table_non_central_t_CDF_complement"></a><p class="title"><b>Table&#160;23.79.&#160;Error rates for non central t CDF complement</b></p>
<div class="table-contents"><table class="table" summary="Error rates for non central t CDF complement">
<colgroup>
<col>
<col>
<col>
<col>
<col>
</colgroup>
<thead><tr>
<th>
              </th>
<th>
                <p>
                  GNU C++ version 7.1.0<br> linux<br> double
                </p>
              </th>
<th>
                <p>
                  GNU C++ version 7.1.0<br> linux<br> long double
                </p>
              </th>
<th>
                <p>
                  Sun compiler version 0x5150<br> Sun Solaris<br> long double
                </p>
              </th>
<th>
                <p>
                  Microsoft Visual C++ version 14.1<br> Win32<br> double
                </p>
              </th>
</tr></thead>
<tbody>
<tr>
<td>
                <p>
                  Non Central T
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 0.707&#949; (Mean = 0.0497&#949;)</span><br>
                  <br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span> <span class="red">Max
                  = 6.19e+15&#949; (Mean = 6.72e+14&#949;) <a class="link" href="logs.html#errors_GNU_C_version_7_1_0_linux_double_non_central_t_CDF_complement_Rmath_3_2_3_Non_Central_T">And
                  other failures.</a>)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 201&#949; (Mean = 31.7&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 340&#949; (Mean = 43.2&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 154&#949; (Mean = 32.1&#949;)</span>
                </p>
              </td>
</tr>
<tr>
<td>
                <p>
                  Non Central T (small non-centrality)
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>Rmath
                  3.2.3:</em></span> Max = 1.87e+03&#949; (Mean = 263&#949;))
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 10.5&#949; (Mean = 2.13&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 10.5&#949; (Mean = 2.39&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 4.6&#949; (Mean = 1.63&#949;)</span>
                </p>
              </td>
</tr>
<tr>
<td>
                <p>
                  Non Central T (large parameters)
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 478&#949; (Mean = 96.3&#949;)</span><br> <br>
                  (<span class="emphasis"><em>Rmath 3.2.3:</em></span> Max = 2.24&#949; (Mean = 0.945&#949;))
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 9.79e+05&#949; (Mean = 1.97e+05&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 9.79e+05&#949; (Mean = 1.97e+05&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 227&#949; (Mean = 50.4&#949;)</span>
                </p>
              </td>
</tr>
</tbody>
</table></div>
</div>
<br class="table-break"><div class="table">
<a name="math_toolkit.logs_and_tables.all_table.table_owens_t"></a><p class="title"><b>Table&#160;23.80.&#160;Error rates for owens_t</b></p>
<div class="table-contents"><table class="table" summary="Error rates for owens_t">
<colgroup>
<col>
<col>
<col>
<col>
<col>
</colgroup>
<thead><tr>
<th>
              </th>
<th>
                <p>
                  GNU C++ version 7.1.0<br> linux<br> double
                </p>
              </th>
<th>
                <p>
                  GNU C++ version 7.1.0<br> linux<br> long double
                </p>
              </th>
<th>
                <p>
                  Sun compiler version 0x5150<br> Sun Solaris<br> long double
                </p>
              </th>
<th>
                <p>
                  Microsoft Visual C++ version 14.1<br> Win32<br> double
                </p>
              </th>
</tr></thead>
<tbody>
<tr>
<td>
                <p>
                  Owens T (medium small values)
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 3.34&#949; (Mean = 0.944&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 3.34&#949; (Mean = 0.911&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 4.37&#949; (Mean = 0.98&#949;)</span>
                </p>
              </td>
</tr>
<tr>
<td>
                <p>
                  Owens T (large and diverse values)
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 49&#949; (Mean = 2.16&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 24.5&#949; (Mean = 1.39&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 3.78&#949; (Mean = 0.621&#949;)</span>
                </p>
              </td>
</tr>
</tbody>
</table></div>
</div>
<br class="table-break"><div class="table">
<a name="math_toolkit.logs_and_tables.all_table.table_polygamma"></a><p class="title"><b>Table&#160;23.81.&#160;Error rates for polygamma</b></p>
<div class="table-contents"><table class="table" summary="Error rates for polygamma">
<colgroup>
<col>
<col>
<col>
<col>
<col>
</colgroup>
<thead><tr>
<th>
              </th>
<th>
                <p>
                  GNU C++ version 7.1.0<br> linux<br> double
                </p>
              </th>
<th>
                <p>
                  GNU C++ version 7.1.0<br> linux<br> long double
                </p>
              </th>
<th>
                <p>
                  Sun compiler version 0x5150<br> Sun Solaris<br> long double
                </p>
              </th>
<th>
                <p>
                  Microsoft Visual C++ version 14.1<br> Win32<br> double
                </p>
              </th>
</tr></thead>
<tbody>
<tr>
<td>
                <p>
                  Mathematica Data
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 0.824&#949; (Mean = 0.0574&#949;)</span><br>
                  <br> (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 62.9&#949; (Mean = 12.8&#949;))<br>
                  (<span class="emphasis"><em>Rmath 3.2.3:</em></span> Max = 108&#949; (Mean = 15.2&#949;))
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 7.38&#949; (Mean = 1.84&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 34.3&#949; (Mean = 7.65&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 9.32&#949; (Mean = 1.95&#949;)</span>
                </p>
              </td>
</tr>
<tr>
<td>
                <p>
                  Mathematica Data - large arguments
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 0.998&#949; (Mean = 0.0592&#949;)</span><br>
                  <br> (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 244&#949; (Mean = 32.8&#949;) <a class="link" href="logs.html#errors_GNU_C_version_7_1_0_linux_double_polygamma_GSL_2_1_Mathematica_Data_large_arguments">And
                  other failures.</a>)<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span>
                  <span class="red">Max = 1.71e+56&#949; (Mean = 1.01e+55&#949;) <a class="link" href="logs.html#errors_GNU_C_version_7_1_0_linux_double_polygamma_Rmath_3_2_3_Mathematica_Data_large_arguments">And
                  other failures.</a>)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 2.23&#949; (Mean = 0.323&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 11.1&#949; (Mean = 0.848&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 150&#949; (Mean = 13.9&#949;)</span>
                </p>
              </td>
</tr>
<tr>
<td>
                <p>
                  Mathematica Data - negative arguments
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 0.516&#949; (Mean = 0.022&#949;)</span><br> <br>
                  (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 36.6&#949; (Mean = 3.04&#949;) <a class="link" href="logs.html#errors_GNU_C_version_7_1_0_linux_double_polygamma_GSL_2_1_Mathematica_Data_negative_arguments">And
                  other failures.</a>)<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span>
                  Max = 0&#949; (Mean = 0&#949;) <a class="link" href="logs.html#errors_GNU_C_version_7_1_0_linux_double_polygamma_Rmath_3_2_3_Mathematica_Data_negative_arguments">And
                  other failures.</a>)
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 269&#949; (Mean = 87.7&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 269&#949; (Mean = 88.4&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 497&#949; (Mean = 129&#949;)</span>
                </p>
              </td>
</tr>
<tr>
<td>
                <p>
                  Mathematica Data - large negative arguments
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
                  2.1:</em></span> Max = 1.79&#949; (Mean = 0.197&#949;) <a class="link" href="logs.html#errors_GNU_C_version_7_1_0_linux_double_polygamma_GSL_2_1_Mathematica_Data_large_negative_arguments">And
                  other failures.</a>)<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span>
                  Max = 0&#949; (Mean = 0&#949;) <a class="link" href="logs.html#errors_GNU_C_version_7_1_0_linux_double_polygamma_Rmath_3_2_3_Mathematica_Data_large_negative_arguments">And
                  other failures.</a>)
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 155&#949; (Mean = 96.4&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 155&#949; (Mean = 96.4&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 162&#949; (Mean = 101&#949;)</span>
                </p>
              </td>
</tr>
<tr>
<td>
                <p>
                  Mathematica Data - small arguments
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
                  2.1:</em></span> Max = 15.2&#949; (Mean = 5.03&#949;))<br> (<span class="emphasis"><em>Rmath
                  3.2.3:</em></span> Max = 106&#949; (Mean = 20&#949;))
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 3.33&#949; (Mean = 0.75&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 3.33&#949; (Mean = 0.75&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 3&#949; (Mean = 0.496&#949;)</span>
                </p>
              </td>
</tr>
<tr>
<td>
                <p>
                  Mathematica Data - Large orders and other bug cases
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
                  2.1:</em></span> Max = 151&#949; (Mean = 39.3&#949;) <a class="link" href="logs.html#errors_GNU_C_version_7_1_0_linux_double_polygamma_GSL_2_1_Mathematica_Data_Large_orders_and_other_bug_cases">And
                  other failures.</a>)<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span>
                  <span class="red">Max = +INF&#949; (Mean = +INF&#949;) <a class="link" href="logs.html#errors_GNU_C_version_7_1_0_linux_double_polygamma_Rmath_3_2_3_Mathematica_Data_Large_orders_and_other_bug_cases">And
                  other failures.</a>)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 54.5&#949; (Mean = 13.3&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 145&#949; (Mean = 55.9&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 200&#949; (Mean = 57.2&#949;)</span>
                </p>
              </td>
</tr>
</tbody>
</table></div>
</div>
<br class="table-break"><div class="table">
<a name="math_toolkit.logs_and_tables.all_table.table_powm1"></a><p class="title"><b>Table&#160;23.82.&#160;Error rates for powm1</b></p>
<div class="table-contents"><table class="table" summary="Error rates for powm1">
<colgroup>
<col>
<col>
<col>
<col>
<col>
</colgroup>
<thead><tr>
<th>
              </th>
<th>
                <p>
                  GNU C++ version 7.1.0<br> linux<br> double
                </p>
              </th>
<th>
                <p>
                  GNU C++ version 7.1.0<br> linux<br> long double
                </p>
              </th>
<th>
                <p>
                  Sun compiler version 0x5150<br> Sun Solaris<br> long double
                </p>
              </th>
<th>
                <p>
                  Microsoft Visual C++ version 14.1<br> Win32<br> double
                </p>
              </th>
</tr></thead>
<tbody><tr>
<td>
                <p>
                  powm1
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 1.06&#949; (Mean = 0.425&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 2.04&#949; (Mean = 0.493&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 1.88&#949; (Mean = 0.49&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 1.84&#949; (Mean = 0.486&#949;)</span>
                </p>
              </td>
</tr></tbody>
</table></div>
</div>
<br class="table-break"><div class="table">
<a name="math_toolkit.logs_and_tables.all_table.table_sin_pi"></a><p class="title"><b>Table&#160;23.83.&#160;Error rates for sin_pi</b></p>
<div class="table-contents"><table class="table" summary="Error rates for sin_pi">
<colgroup>
<col>
<col>
<col>
<col>
<col>
</colgroup>
<thead><tr>
<th>
              </th>
<th>
                <p>
                  GNU C++ version 7.1.0<br> linux<br> double
                </p>
              </th>
<th>
                <p>
                  GNU C++ version 7.1.0<br> linux<br> long double
                </p>
              </th>
<th>
                <p>
                  Sun compiler version 0x5150<br> Sun Solaris<br> long double
                </p>
              </th>
<th>
                <p>
                  Microsoft Visual C++ version 14.1<br> Win32<br> double
                </p>
              </th>
</tr></thead>
<tbody>
<tr>
<td>
                <p>
                  sin_pi and cos_pi
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 0.996&#949; (Mean = 0.335&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 0.996&#949; (Mean = 0.336&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 0.99&#949; (Mean = 0.328&#949;)</span>
                </p>
              </td>
</tr>
<tr>
<td>
                <p>
                  sin_pi and cos_pi near integers and half integers
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 0.976&#949; (Mean = 0.293&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 0.976&#949; (Mean = 0.293&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 0.996&#949; (Mean = 0.343&#949;)</span>
                </p>
              </td>
</tr>
</tbody>
</table></div>
</div>
<br class="table-break"><div class="table">
<a name="math_toolkit.logs_and_tables.all_table.table_sph_bessel"></a><p class="title"><b>Table&#160;23.84.&#160;Error rates for sph_bessel</b></p>
<div class="table-contents"><table class="table" summary="Error rates for sph_bessel">
<colgroup>
<col>
<col>
<col>
<col>
<col>
</colgroup>
<thead><tr>
<th>
              </th>
<th>
                <p>
                  GNU C++ version 7.1.0<br> linux<br> long double
                </p>
              </th>
<th>
                <p>
                  GNU C++ version 7.1.0<br> linux<br> double
                </p>
              </th>
<th>
                <p>
                  Sun compiler version 0x5150<br> Sun Solaris<br> long double
                </p>
              </th>
<th>
                <p>
                  Microsoft Visual C++ version 14.1<br> Win32<br> double
                </p>
              </th>
</tr></thead>
<tbody><tr>
<td>
                <p>
                  Bessel j: Random Data
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 243&#949; (Mean = 13.3&#949;)</span><br> <br>
                  (<span class="emphasis"><em>&lt;cmath&gt;:</em></span> Max = 1.91e+06&#949; (Mean = 1.09e+05&#949;))
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 0.978&#949; (Mean = 0.0445&#949;)</span><br>
                  <br> (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 1.79e+03&#949; (Mean = 107&#949;))
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 243&#949; (Mean = 33.7&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 245&#949; (Mean = 16.3&#949;)</span>
                </p>
              </td>
</tr></tbody>
</table></div>
</div>
<br class="table-break"><div class="table">
<a name="math_toolkit.logs_and_tables.all_table.table_sph_bessel_prime"></a><p class="title"><b>Table&#160;23.85.&#160;Error rates for sph_bessel_prime</b></p>
<div class="table-contents"><table class="table" summary="Error rates for sph_bessel_prime">
<colgroup>
<col>
<col>
<col>
<col>
<col>
</colgroup>
<thead><tr>
<th>
              </th>
<th>
                <p>
                  GNU C++ version 7.1.0<br> linux<br> double
                </p>
              </th>
<th>
                <p>
                  GNU C++ version 7.1.0<br> linux<br> long double
                </p>
              </th>
<th>
                <p>
                  Sun compiler version 0x5150<br> Sun Solaris<br> long double
                </p>
              </th>
<th>
                <p>
                  Microsoft Visual C++ version 14.1<br> Win32<br> double
                </p>
              </th>
</tr></thead>
<tbody><tr>
<td>
                <p>
                  Bessel j': Random Data
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 0.753&#949; (Mean = 0.0343&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 167&#949; (Mean = 12&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 167&#949; (Mean = 33.2&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 307&#949; (Mean = 25.2&#949;)</span>
                </p>
              </td>
</tr></tbody>
</table></div>
</div>
<br class="table-break"><div class="table">
<a name="math_toolkit.logs_and_tables.all_table.table_sph_neumann"></a><p class="title"><b>Table&#160;23.86.&#160;Error rates for sph_neumann</b></p>
<div class="table-contents"><table class="table" summary="Error rates for sph_neumann">
<colgroup>
<col>
<col>
<col>
<col>
<col>
</colgroup>
<thead><tr>
<th>
              </th>
<th>
                <p>
                  GNU C++ version 7.1.0<br> linux<br> long double
                </p>
              </th>
<th>
                <p>
                  GNU C++ version 7.1.0<br> linux<br> double
                </p>
              </th>
<th>
                <p>
                  Sun compiler version 0x5150<br> Sun Solaris<br> long double
                </p>
              </th>
<th>
                <p>
                  Microsoft Visual C++ version 14.1<br> Win32<br> double
                </p>
              </th>
</tr></thead>
<tbody><tr>
<td>
                <p>
                  y: Random Data
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 234&#949; (Mean = 19.5&#949;)</span><br> <br>
                  (<span class="emphasis"><em>&lt;cmath&gt;:</em></span> Max = 1.6e+06&#949; (Mean = 1.4e+05&#949;))
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 0.995&#949; (Mean = 0.0665&#949;)</span><br>
                  <br> (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 8.5e+04&#949; (Mean = 5.33e+03&#949;))
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 234&#949; (Mean = 19.8&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 281&#949; (Mean = 31.1&#949;)</span>
                </p>
              </td>
</tr></tbody>
</table></div>
</div>
<br class="table-break"><div class="table">
<a name="math_toolkit.logs_and_tables.all_table.table_sph_neumann_prime"></a><p class="title"><b>Table&#160;23.87.&#160;Error rates for sph_neumann_prime</b></p>
<div class="table-contents"><table class="table" summary="Error rates for sph_neumann_prime">
<colgroup>
<col>
<col>
<col>
<col>
<col>
</colgroup>
<thead><tr>
<th>
              </th>
<th>
                <p>
                  GNU C++ version 7.1.0<br> linux<br> double
                </p>
              </th>
<th>
                <p>
                  GNU C++ version 7.1.0<br> linux<br> long double
                </p>
              </th>
<th>
                <p>
                  Sun compiler version 0x5150<br> Sun Solaris<br> long double
                </p>
              </th>
<th>
                <p>
                  Microsoft Visual C++ version 14.1<br> Win32<br> double
                </p>
              </th>
</tr></thead>
<tbody><tr>
<td>
                <p>
                  y': Random Data
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 0.988&#949; (Mean = 0.0869&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 158&#949; (Mean = 18.8&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 158&#949; (Mean = 20.2&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 296&#949; (Mean = 25.6&#949;)</span>
                </p>
              </td>
</tr></tbody>
</table></div>
</div>
<br class="table-break"><div class="table">
<a name="math_toolkit.logs_and_tables.all_table.table_spherical_harmonic_i"></a><p class="title"><b>Table&#160;23.88.&#160;Error rates for spherical_harmonic_i</b></p>
<div class="table-contents"><table class="table" summary="Error rates for spherical_harmonic_i">
<colgroup>
<col>
<col>
<col>
<col>
<col>
</colgroup>
<thead><tr>
<th>
              </th>
<th>
                <p>
                  GNU C++ version 7.1.0<br> linux<br> double
                </p>
              </th>
<th>
                <p>
                  GNU C++ version 7.1.0<br> linux<br> long double
                </p>
              </th>
<th>
                <p>
                  Sun compiler version 0x5150<br> Sun Solaris<br> long double
                </p>
              </th>
<th>
                <p>
                  Microsoft Visual C++ version 14.1<br> Win32<br> double
                </p>
              </th>
</tr></thead>
<tbody><tr>
<td>
                <p>
                  Spherical Harmonics
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 1.36&#949; (Mean = 0.0765&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 2.89e+03&#949; (Mean = 108&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 1.03e+04&#949; (Mean = 327&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 2.27e+04&#949; (Mean = 725&#949;)</span>
                </p>
              </td>
</tr></tbody>
</table></div>
</div>
<br class="table-break"><div class="table">
<a name="math_toolkit.logs_and_tables.all_table.table_spherical_harmonic_r"></a><p class="title"><b>Table&#160;23.89.&#160;Error rates for spherical_harmonic_r</b></p>
<div class="table-contents"><table class="table" summary="Error rates for spherical_harmonic_r">
<colgroup>
<col>
<col>
<col>
<col>
<col>
</colgroup>
<thead><tr>
<th>
              </th>
<th>
                <p>
                  GNU C++ version 7.1.0<br> linux<br> double
                </p>
              </th>
<th>
                <p>
                  GNU C++ version 7.1.0<br> linux<br> long double
                </p>
              </th>
<th>
                <p>
                  Sun compiler version 0x5150<br> Sun Solaris<br> long double
                </p>
              </th>
<th>
                <p>
                  Microsoft Visual C++ version 14.1<br> Win32<br> double
                </p>
              </th>
</tr></thead>
<tbody><tr>
<td>
                <p>
                  Spherical Harmonics
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 1.58&#949; (Mean = 0.0707&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 2.89e+03&#949; (Mean = 108&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 1.03e+04&#949; (Mean = 327&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 2.27e+04&#949; (Mean = 725&#949;)</span>
                </p>
              </td>
</tr></tbody>
</table></div>
</div>
<br class="table-break"><div class="table">
<a name="math_toolkit.logs_and_tables.all_table.table_sqrt1pm1"></a><p class="title"><b>Table&#160;23.90.&#160;Error rates for sqrt1pm1</b></p>
<div class="table-contents"><table class="table" summary="Error rates for sqrt1pm1">
<colgroup>
<col>
<col>
<col>
<col>
<col>
</colgroup>
<thead><tr>
<th>
              </th>
<th>
                <p>
                  GNU C++ version 7.1.0<br> linux<br> double
                </p>
              </th>
<th>
                <p>
                  GNU C++ version 7.1.0<br> linux<br> long double
                </p>
              </th>
<th>
                <p>
                  Sun compiler version 0x5150<br> Sun Solaris<br> long double
                </p>
              </th>
<th>
                <p>
                  Microsoft Visual C++ version 14.1<br> Win32<br> double
                </p>
              </th>
</tr></thead>
<tbody><tr>
<td>
                <p>
                  sqrt1pm1
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 1.3&#949; (Mean = 0.404&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 1.33&#949; (Mean = 0.404&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 1.54&#949; (Mean = 0.563&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 1.35&#949; (Mean = 0.497&#949;)</span>
                </p>
              </td>
</tr></tbody>
</table></div>
</div>
<br class="table-break"><div class="table">
<a name="math_toolkit.logs_and_tables.all_table.table_tgamma"></a><p class="title"><b>Table&#160;23.91.&#160;Error rates for tgamma</b></p>
<div class="table-contents"><table class="table" summary="Error rates for tgamma">
<colgroup>
<col>
<col>
<col>
<col>
<col>
</colgroup>
<thead><tr>
<th>
              </th>
<th>
                <p>
                  GNU C++ version 7.1.0<br> linux<br> double
                </p>
              </th>
<th>
                <p>
                  GNU C++ version 7.1.0<br> linux<br> long double
                </p>
              </th>
<th>
                <p>
                  Sun compiler version 0x5150<br> Sun Solaris<br> long double
                </p>
              </th>
<th>
                <p>
                  Microsoft Visual C++ version 14.1<br> Win32<br> double
                </p>
              </th>
</tr></thead>
<tbody>
<tr>
<td>
                <p>
                  factorials
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
                  2.1:</em></span> Max = 3.95&#949; (Mean = 0.783&#949;))<br> (<span class="emphasis"><em>Rmath
                  3.2.3:</em></span> Max = 314&#949; (Mean = 93.4&#949;))
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 2.67&#949; (Mean = 0.617&#949;)</span><br> <br>
                  (<span class="emphasis"><em>&lt;cmath&gt;:</em></span> Max = 1.66&#949; (Mean = 0.584&#949;))<br>
                  (<span class="emphasis"><em>&lt;math.h&gt;:</em></span> Max = 1.66&#949; (Mean = 0.584&#949;))
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 172&#949; (Mean = 41&#949;)</span><br> <br>
                  (<span class="emphasis"><em>&lt;math.h&gt;:</em></span> Max = 0&#949; (Mean = 0&#949;))
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 1.85&#949; (Mean = 0.566&#949;)</span><br> <br>
                  (<span class="emphasis"><em>&lt;math.h&gt;:</em></span> Max = 3.17&#949; (Mean = 0.928&#949;))
                </p>
              </td>
</tr>
<tr>
<td>
                <p>
                  near 0
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
                  2.1:</em></span> Max = 4.51&#949; (Mean = 1.92&#949;))<br> (<span class="emphasis"><em>Rmath
                  3.2.3:</em></span> Max = 1&#949; (Mean = 0.335&#949;))
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 2&#949; (Mean = 0.608&#949;)</span><br> <br>
                  (<span class="emphasis"><em>&lt;cmath&gt;:</em></span> Max = 1&#949; (Mean = 0.376&#949;))<br>
                  (<span class="emphasis"><em>&lt;math.h&gt;:</em></span> Max = 1&#949; (Mean = 0.376&#949;))
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 2&#949; (Mean = 0.647&#949;)</span><br> <br>
                  (<span class="emphasis"><em>&lt;math.h&gt;:</em></span> Max = 0.5&#949; (Mean = 0.0791&#949;))
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 1.5&#949; (Mean = 0.635&#949;)</span><br> <br>
                  (<span class="emphasis"><em>&lt;math.h&gt;:</em></span> Max = 1&#949; (Mean = 0.405&#949;))
                </p>
              </td>
</tr>
<tr>
<td>
                <p>
                  near 1
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
                  2.1:</em></span> Max = 4.41&#949; (Mean = 1.81&#949;))<br> (<span class="emphasis"><em>Rmath
                  3.2.3:</em></span> Max = 1&#949; (Mean = 0.32&#949;))
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 2.51&#949; (Mean = 1.02&#949;)</span><br> <br>
                  (<span class="emphasis"><em>&lt;cmath&gt;:</em></span> Max = 0.918&#949; (Mean = 0.203&#949;))<br>
                  (<span class="emphasis"><em>&lt;math.h&gt;:</em></span> Max = 0.918&#949; (Mean = 0.203&#949;))
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 3.01&#949; (Mean = 1.06&#949;)</span><br> <br>
                  (<span class="emphasis"><em>&lt;math.h&gt;:</em></span> Max = 1&#949; (Mean = 0.175&#949;))
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 1.1&#949; (Mean = 0.59&#949;)</span><br> <br>
                  (<span class="emphasis"><em>&lt;math.h&gt;:</em></span> Max = 1&#949; (Mean = 0.4&#949;))
                </p>
              </td>
</tr>
<tr>
<td>
                <p>
                  near 2
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
                  2.1:</em></span> Max = 7.95&#949; (Mean = 3.12&#949;))<br> (<span class="emphasis"><em>Rmath
                  3.2.3:</em></span> Max = 1&#949; (Mean = 0.191&#949;))
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 4.1&#949; (Mean = 1.55&#949;)</span><br> <br>
                  (<span class="emphasis"><em>&lt;cmath&gt;:</em></span> Max = 0.558&#949; (Mean = 0.298&#949;))<br>
                  (<span class="emphasis"><em>&lt;math.h&gt;:</em></span> Max = 0.558&#949; (Mean = 0.298&#949;))
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 5.01&#949; (Mean = 1.89&#949;)</span><br> <br>
                  (<span class="emphasis"><em>&lt;math.h&gt;:</em></span> Max = 0&#949; (Mean = 0&#949;))
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 2&#949; (Mean = 0.733&#949;)</span><br> <br>
                  (<span class="emphasis"><em>&lt;math.h&gt;:</em></span> Max = 0&#949; (Mean = 0&#949;))
                </p>
              </td>
</tr>
<tr>
<td>
                <p>
                  near -10
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
                  2.1:</em></span> Max = 2.6&#949; (Mean = 1.05&#949;))<br> (<span class="emphasis"><em>Rmath
                  3.2.3:</em></span> Max = 34.9&#949; (Mean = 9.2&#949;))
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 1.75&#949; (Mean = 0.895&#949;)</span><br> <br>
                  (<span class="emphasis"><em>&lt;cmath&gt;:</em></span> Max = 2.26&#949; (Mean = 1.08&#949;))<br>
                  (<span class="emphasis"><em>&lt;math.h&gt;:</em></span> Max = 2.26&#949; (Mean = 1.08&#949;))
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 1.75&#949; (Mean = 0.819&#949;)</span><br> <br>
                  (<span class="emphasis"><em>&lt;math.h&gt;:</em></span> Max = 0&#949; (Mean = 0&#949;))
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 1.86&#949; (Mean = 0.881&#949;)</span><br> <br>
                  (<span class="emphasis"><em>&lt;math.h&gt;:</em></span> Max = 0.866&#949; (Mean = 0.445&#949;))
                </p>
              </td>
</tr>
<tr>
<td>
                <p>
                  near -55
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
                  2.1:</em></span> Max = 1.8&#949; (Mean = 0.782&#949;))<br> (<span class="emphasis"><em>Rmath
                  3.2.3:</em></span> Max = 3.89e+04&#949; (Mean = 9.52e+03&#949;))
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 2.69&#949; (Mean = 1.09&#949;)</span><br> <br>
                  (<span class="emphasis"><em>&lt;cmath&gt;:</em></span> Max = 1.79&#949; (Mean = 0.75&#949;))<br>
                  (<span class="emphasis"><em>&lt;math.h&gt;:</em></span> Max = 1.79&#949; (Mean = 0.75&#949;))
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 98.5&#949; (Mean = 53.4&#949;)</span><br> <br>
                  (<span class="emphasis"><em>&lt;math.h&gt;:</em></span> Max = 0&#949; (Mean = 0&#949;))
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 2.7&#949; (Mean = 1.35&#949;)</span><br> <br>
                  (<span class="emphasis"><em>&lt;math.h&gt;:</em></span> Max = 3.87e+04&#949; (Mean = 6.71e+03&#949;))
                </p>
              </td>
</tr>
</tbody>
</table></div>
</div>
<br class="table-break"><div class="table">
<a name="math_toolkit.logs_and_tables.all_table.table_tgamma1pm1"></a><p class="title"><b>Table&#160;23.92.&#160;Error rates for tgamma1pm1</b></p>
<div class="table-contents"><table class="table" summary="Error rates for tgamma1pm1">
<colgroup>
<col>
<col>
<col>
<col>
<col>
</colgroup>
<thead><tr>
<th>
              </th>
<th>
                <p>
                  GNU C++ version 7.1.0<br> linux<br> double
                </p>
              </th>
<th>
                <p>
                  GNU C++ version 7.1.0<br> linux<br> long double
                </p>
              </th>
<th>
                <p>
                  Sun compiler version 0x5150<br> Sun Solaris<br> long double
                </p>
              </th>
<th>
                <p>
                  Microsoft Visual C++ version 14.1<br> Win32<br> double
                </p>
              </th>
</tr></thead>
<tbody><tr>
<td>
                <p>
                  tgamma1pm1(dz)
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 1.12&#949; (Mean = 0.49&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 6.61&#949; (Mean = 0.84&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 3.31&#949; (Mean = 0.517&#949;)</span>
                </p>
              </td>
</tr></tbody>
</table></div>
</div>
<br class="table-break"><div class="table">
<a name="math_toolkit.logs_and_tables.all_table.table_tgamma_delta_ratio"></a><p class="title"><b>Table&#160;23.93.&#160;Error rates for tgamma_delta_ratio</b></p>
<div class="table-contents"><table class="table" summary="Error rates for tgamma_delta_ratio">
<colgroup>
<col>
<col>
<col>
<col>
<col>
</colgroup>
<thead><tr>
<th>
              </th>
<th>
                <p>
                  GNU C++ version 7.1.0<br> linux<br> double
                </p>
              </th>
<th>
                <p>
                  GNU C++ version 7.1.0<br> linux<br> long double
                </p>
              </th>
<th>
                <p>
                  Sun compiler version 0x5150<br> Sun Solaris<br> long double
                </p>
              </th>
<th>
                <p>
                  Microsoft Visual C++ version 14.1<br> Win32<br> double
                </p>
              </th>
</tr></thead>
<tbody>
<tr>
<td>
                <p>
                  tgamma + small delta ratios
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 5.83&#949; (Mean = 1.3&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 15.4&#949; (Mean = 2.09&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 7.56&#949; (Mean = 1.31&#949;)</span>
                </p>
              </td>
</tr>
<tr>
<td>
                <p>
                  tgamma + small delta ratios (negative delta)
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 7.94&#949; (Mean = 1.4&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 18.3&#949; (Mean = 2.03&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 7.43&#949; (Mean = 1.42&#949;)</span>
                </p>
              </td>
</tr>
<tr>
<td>
                <p>
                  tgamma + small integer ratios
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 1.96&#949; (Mean = 0.677&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 1.96&#949; (Mean = 0.677&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 2.74&#949; (Mean = 0.736&#949;)</span>
                </p>
              </td>
</tr>
<tr>
<td>
                <p>
                  tgamma + small integer ratios (negative delta)
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 1.62&#949; (Mean = 0.451&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 1.62&#949; (Mean = 0.451&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 2.15&#949; (Mean = 0.685&#949;)</span>
                </p>
              </td>
</tr>
<tr>
<td>
                <p>
                  integer tgamma ratios
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 0.997&#949; (Mean = 0.4&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 0.997&#949; (Mean = 0.4&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 0.968&#949; (Mean = 0.386&#949;)</span>
                </p>
              </td>
</tr>
<tr>
<td>
                <p>
                  integer tgamma ratios (negative delta)
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 0.853&#949; (Mean = 0.176&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 0.853&#949; (Mean = 0.176&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 0.974&#949; (Mean = 0.175&#949;)</span>
                </p>
              </td>
</tr>
</tbody>
</table></div>
</div>
<br class="table-break"><div class="table">
<a name="math_toolkit.logs_and_tables.all_table.table_tgamma_incomplete_"></a><p class="title"><b>Table&#160;23.94.&#160;Error rates for tgamma (incomplete)</b></p>
<div class="table-contents"><table class="table" summary="Error rates for tgamma (incomplete)">
<colgroup>
<col>
<col>
<col>
<col>
<col>
</colgroup>
<thead><tr>
<th>
              </th>
<th>
                <p>
                  GNU C++ version 7.1.0<br> linux<br> double
                </p>
              </th>
<th>
                <p>
                  GNU C++ version 7.1.0<br> linux<br> long double
                </p>
              </th>
<th>
                <p>
                  Sun compiler version 0x5150<br> Sun Solaris<br> long double
                </p>
              </th>
<th>
                <p>
                  Microsoft Visual C++ version 14.1<br> Win32<br> double
                </p>
              </th>
</tr></thead>
<tbody>
<tr>
<td>
                <p>
                  tgamma(a, z) medium values
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
                  2.1:</em></span> Max = 200&#949; (Mean = 13.3&#949;))
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 8.47&#949; (Mean = 1.9&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 412&#949; (Mean = 95.5&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 8.14&#949; (Mean = 1.76&#949;)</span>
                </p>
              </td>
</tr>
<tr>
<td>
                <p>
                  tgamma(a, z) small values
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 0.753&#949; (Mean = 0.0474&#949;)</span><br>
                  <br> (<span class="emphasis"><em>GSL 2.1:</em></span> <span class="red">Max =
                  1.38e+10&#949; (Mean = 1.05e+09&#949;))</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 2.31&#949; (Mean = 0.775&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 2.13&#949; (Mean = 0.717&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 2.53&#949; (Mean = 0.66&#949;)</span>
                </p>
              </td>
</tr>
<tr>
<td>
                <p>
                  tgamma(a, z) integer and half integer values
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
                  2.1:</em></span> Max = 117&#949; (Mean = 12.5&#949;))
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 5.52&#949; (Mean = 1.48&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 79.6&#949; (Mean = 20.9&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 5.16&#949; (Mean = 1.33&#949;)</span>
                </p>
              </td>
</tr>
</tbody>
</table></div>
</div>
<br class="table-break"><div class="table">
<a name="math_toolkit.logs_and_tables.all_table.table_tgamma_lower"></a><p class="title"><b>Table&#160;23.95.&#160;Error rates for tgamma_lower</b></p>
<div class="table-contents"><table class="table" summary="Error rates for tgamma_lower">
<colgroup>
<col>
<col>
<col>
<col>
<col>
</colgroup>
<thead><tr>
<th>
              </th>
<th>
                <p>
                  GNU C++ version 7.1.0<br> linux<br> double
                </p>
              </th>
<th>
                <p>
                  GNU C++ version 7.1.0<br> linux<br> long double
                </p>
              </th>
<th>
                <p>
                  Sun compiler version 0x5150<br> Sun Solaris<br> long double
                </p>
              </th>
<th>
                <p>
                  Microsoft Visual C++ version 14.1<br> Win32<br> double
                </p>
              </th>
</tr></thead>
<tbody>
<tr>
<td>
                <p>
                  tgamma(a, z) medium values
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 0.833&#949; (Mean = 0.0315&#949;)</span><br>
                  <br> (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 0.833&#949; (Mean = 0.0315&#949;))
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 6.79&#949; (Mean = 1.46&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 363&#949; (Mean = 63.8&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 5.62&#949; (Mean = 1.49&#949;)</span>
                </p>
              </td>
</tr>
<tr>
<td>
                <p>
                  tgamma(a, z) small values
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
                  2.1:</em></span> Max = 0&#949; (Mean = 0&#949;))
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 1.97&#949; (Mean = 0.555&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 1.97&#949; (Mean = 0.558&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 1.57&#949; (Mean = 0.525&#949;)</span>
                </p>
              </td>
</tr>
<tr>
<td>
                <p>
                  tgamma(a, z) integer and half integer values
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
                  2.1:</em></span> Max = 0&#949; (Mean = 0&#949;))
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 4.83&#949; (Mean = 1.15&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 84.7&#949; (Mean = 17.5&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 2.69&#949; (Mean = 0.849&#949;)</span>
                </p>
              </td>
</tr>
</tbody>
</table></div>
</div>
<br class="table-break"><div class="table">
<a name="math_toolkit.logs_and_tables.all_table.table_tgamma_ratio"></a><p class="title"><b>Table&#160;23.96.&#160;Error rates for tgamma_ratio</b></p>
<div class="table-contents"><table class="table" summary="Error rates for tgamma_ratio">
<colgroup>
<col>
<col>
<col>
<col>
<col>
</colgroup>
<thead><tr>
<th>
              </th>
<th>
                <p>
                  GNU C++ version 7.1.0<br> linux<br> double
                </p>
              </th>
<th>
                <p>
                  GNU C++ version 7.1.0<br> linux<br> long double
                </p>
              </th>
<th>
                <p>
                  Sun compiler version 0x5150<br> Sun Solaris<br> long double
                </p>
              </th>
<th>
                <p>
                  Microsoft Visual C++ version 14.1<br> Win32<br> double
                </p>
              </th>
</tr></thead>
<tbody><tr>
<td>
                <p>
                  tgamma ratios
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 0.694&#949; (Mean = 0.0347&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 2.99&#949; (Mean = 1.15&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 174&#949; (Mean = 61.2&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 3.28&#949; (Mean = 1.12&#949;)</span>
                </p>
              </td>
</tr></tbody>
</table></div>
</div>
<br class="table-break"><div class="table">
<a name="math_toolkit.logs_and_tables.all_table.table_trigamma"></a><p class="title"><b>Table&#160;23.97.&#160;Error rates for trigamma</b></p>
<div class="table-contents"><table class="table" summary="Error rates for trigamma">
<colgroup>
<col>
<col>
<col>
<col>
<col>
</colgroup>
<thead><tr>
<th>
              </th>
<th>
                <p>
                  GNU C++ version 7.1.0<br> linux<br> double
                </p>
              </th>
<th>
                <p>
                  GNU C++ version 7.1.0<br> linux<br> long double
                </p>
              </th>
<th>
                <p>
                  Sun compiler version 0x5150<br> Sun Solaris<br> long double
                </p>
              </th>
<th>
                <p>
                  Microsoft Visual C++ version 14.1<br> Win32<br> double
                </p>
              </th>
</tr></thead>
<tbody><tr>
<td>
                <p>
                  Mathematica Data
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 0.998&#949; (Mean = 0.105&#949;)</span><br> <br>
                  (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 1.34e+04&#949; (Mean = 1.49e+03&#949;))<br>
                  (<span class="emphasis"><em>Rmath 3.2.3:</em></span> Max = 1.34e+04&#949; (Mean = 1.51e+03&#949;))
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 1.28&#949; (Mean = 0.449&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 1.28&#949; (Mean = 0.449&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 1&#949; (Mean = 0.382&#949;)</span>
                </p>
              </td>
</tr></tbody>
</table></div>
</div>
<br class="table-break"><div class="table">
<a name="math_toolkit.logs_and_tables.all_table.table_zeta"></a><p class="title"><b>Table&#160;23.98.&#160;Error rates for zeta</b></p>
<div class="table-contents"><table class="table" summary="Error rates for zeta">
<colgroup>
<col>
<col>
<col>
<col>
<col>
</colgroup>
<thead><tr>
<th>
              </th>
<th>
                <p>
                  GNU C++ version 7.1.0<br> linux<br> long double
                </p>
              </th>
<th>
                <p>
                  GNU C++ version 7.1.0<br> linux<br> double
                </p>
              </th>
<th>
                <p>
                  Sun compiler version 0x5150<br> Sun Solaris<br> long double
                </p>
              </th>
<th>
                <p>
                  Microsoft Visual C++ version 14.1<br> Win32<br> double
                </p>
              </th>
</tr></thead>
<tbody>
<tr>
<td>
                <p>
                  Zeta: Random values greater than 1
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 0.846&#949; (Mean = 0.0833&#949;)</span><br>
                  <br> (<span class="emphasis"><em>&lt;cmath&gt;:</em></span> Max = 5.45&#949; (Mean = 1&#949;))
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
                  2.1:</em></span> Max = 8.69&#949; (Mean = 1.03&#949;))
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 0.846&#949; (Mean = 0.0833&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 0.836&#949; (Mean = 0.093&#949;)</span>
                </p>
              </td>
</tr>
<tr>
<td>
                <p>
                  Zeta: Random values less than 1
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 7.03&#949; (Mean = 2.93&#949;)</span><br> <br>
                  (<span class="emphasis"><em>&lt;cmath&gt;:</em></span> Max = 538&#949; (Mean = 59.3&#949;))
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
                  2.1:</em></span> Max = 137&#949; (Mean = 13.8&#949;))
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 70.1&#949; (Mean = 17.1&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 6.84&#949; (Mean = 3.12&#949;)</span>
                </p>
              </td>
</tr>
<tr>
<td>
                <p>
                  Zeta: Values close to and greater than 1
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 0.995&#949; (Mean = 0.5&#949;)</span><br> <br>
                  (<span class="emphasis"><em>&lt;cmath&gt;:</em></span> Max = 1.9e+06&#949; (Mean = 5.11e+05&#949;))
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
                  2.1:</em></span> Max = 7.73&#949; (Mean = 4.07&#949;))
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 0.995&#949; (Mean = 0.5&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 0.994&#949; (Mean = 0.421&#949;)</span>
                </p>
              </td>
</tr>
<tr>
<td>
                <p>
                  Zeta: Values close to and less than 1
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 0.998&#949; (Mean = 0.508&#949;)</span><br> <br>
                  (<span class="emphasis"><em>&lt;cmath&gt;:</em></span> Max = 8.53e+06&#949; (Mean = 1.87e+06&#949;))
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
                  2.1:</em></span> Max = 0.991&#949; (Mean = 0.28&#949;))
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 0.998&#949; (Mean = 0.508&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 0.991&#949; (Mean = 0.375&#949;)</span>
                </p>
              </td>
</tr>
<tr>
<td>
                <p>
                  Zeta: Integer arguments
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 9&#949; (Mean = 3.06&#949;)</span><br> <br>
                  (<span class="emphasis"><em>&lt;cmath&gt;:</em></span> Max = 70.3&#949; (Mean = 17.4&#949;))
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>GSL
                  2.1:</em></span> Max = 3.75&#949; (Mean = 1.1&#949;))
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 28&#949; (Mean = 5.62&#949;)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 9&#949; (Mean = 3&#949;)</span>
                </p>
              </td>
</tr>
</tbody>
</table></div>
</div>
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<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2019 Nikhar
      Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan
      R&#229;de, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
      Daryle Walker and Xiaogang Zhang<p>
        Distributed under the Boost Software License, Version 1.0. (See accompanying
        file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
      </p>
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